Every AC unit dehumidifies when cooling is on. I'm just wondering why dehumidification only is not an option, as is in standalone dehumidifiers? E.g. my basement stays pretty cool even in the summer but humidity can easily be 60-70%. I would like to run the dehumidifier in its dedicated AC unit without necessarily cooling but not have a standalone dehumidifier that has to have water drained separately. But to get it in the 40-50% range using AC, I would need to also cool the place to around 60°.
Dehumidifiers work a bit different than A/C units. While A/C units do remove moisture, as a side effect. They also cool the air moving through them, by moving heat away. Dehumidifiers remove the moisture and cool the air, but then they heat the air back up.
If you wanted your A/C system to function as a dehumidifier, you'd have to bring back the heat that was removed from the air. This is possible with a package unit, but would be quite difficult with a split system.
The coil on a good dehumidifier is SIGNIFICANTLY colder than the coil on a typical air conditioner.
A typical central AC unit is configured so the air coming off the coil is approximately 20 degrees (F) colder than the air entering the coil, and tends to be somewhere in the neighborhood of 52-55 degrees (F).
As the air passes over the coil, water below the coil temperature's dew point condenses onto the coil and drips off into the drain pan. When 52F air at 100% RH warms to 72F, its humidity falls to 50%. If it rises to 80F, its humidity falls to 38%.
HOWEVER... if your goal is 72F air that's drier than 50%, or 80F air that's drier than 38%, you need a colder coil. To get 72F air down to 30%RH (or get 80F air down to 23F), the coil temperature needs to be ~39F.
(For more info, Google 'psychrometric chart')
This is why cheap dehumidifiers throw off a lot of heat, but still can't seem to get the room much below 50% RH... and why most typical central AC systems feel clammy at temperatures below 74F. As the temperature falls, they become incapable of wringing enough humidity out of the air to make it feel dry.
This is also why most window air conditioners leave the room feeling humid at ANY temperature... they just don't get cold enough to properly dehumidify the air, especially at colder temperatures.
This also reveals a nifty hack you can do with some central AC units to radically improve their humidity-removal (at the expense of significantly higher power consumption, and a possible risk of freezing the coil if you aren't careful). If you slow down the air moving over the coil (by reducing the speed of the blower fan), the coil gets colder, and more humidity gets removed from the air.
If your central AC has an "ECM" type motor, read its service manual carefully... especially the part about low-voltage/control wiring. There's an EXCELLENT possibility that it has a jumper/DIP switch/terminal (probably marked "Dh", "DEHU", or "Dehumidistat") that's normally closed, but when open will reduce the blower speed to ~80% of normal. By removing the jumper and opening the contacts, you can get the humidity a good 5-10% lower that you'd otherwise be able to achieve.
On SOME systems, particularly Carrier/Bryant with "PerfectHumidity", there's another option... if you close "red" to "yellow" (powering up the condenser) while leaving green (blower fan) open, it'll reduce the blower speed to 60% of normal. Normally, this mode only gets unlocked if you buy their expensive custom thermostat... but it's fun to play with if you're aware of its limitations. Namely, in that mode, your system will probably run 100% of the time for hours and hours whenever the temperature gets much above 90F. Latent-heat removal is nice, but when it's REALLY hot outside, sometimes you have to sacrifice a bit of latent-heat removal for brute-force sensible-heat removal. You're also at extreme risk of having the coils eventually ice up after a few hours of running like this... the coil gets so cold, and the air is so humid, eventually the condensate starts to freeze in place on the coils before it even has TIME to bead up and drip off into the pan.
I believe Thermostats like Ecobee and Nest support the 80%-vs-100% mode on systems that are capable of it, but AFAIK, only Carrier's proprietary thermostats properly use "Super-Dehumidify" mode.
Aside from being able to achieve extreme dehumidification, the reduced-speed modes serve another purpose: they allow you to extend your running time on days when it's humid, but not particularly hot. This is where Carrier's "Super Dehumidify" mode REALLY shines... on a cold February day when it's 62F outside, rainy, the AC hasn't cycled on for more than a few minutes at a time all day (because it's technically 72 inside), and the humidity is becoming oppressive, 20 minutes per hour in S-D mode can work miracles for dehumidifying your house.
Just to add an additional disclaimer, there's another factor to consider when attempting extreme dehumidification using central AC alone. Modern evaporator coils (the part that cools the air as it passes through it) have significantly denser cooling fins than old units did, which combines with the surface tension of water to leave the coil a lot "wetter" than they used to be on older systems. If your system is programmed for maximum energy-efficiency & keeps the blower running for 90 seconds after turning off the compressor (the EnergyStar-mandated default), half the water that was pulled out of the air by the coils is going to get evaporated right back into the house. To prevent it, search your air conditioner's service manual. If you're lucky, there will be jumper settings on the circuit board (or in the installer menu, if you're using a proprietary communicating-type thermostat) to delay turning on the blower fan until a few seconds AFTER the compressor starts and the coils become cold, and to eliminate (or at least, reduce to something like 5-10 seconds) the delay before the the blower turns off after shutting off the compressor.
The phenomenon of having the coil freeze during extended run cycles is well known, and is the reason why heat pumps have an explicit 'defrost' mode. Grossly oversimplifying, a heat pump heats a house by air-conditioning the outside and dumping the waste heat inside. Running a heat pump (in heating mode) for hours and hours at a time when it's already cold & humid outside is basically the same situation as running an air conditioner at low blower speed with cold, humid air for hours and hours at a time. The difference is, with heat pumps, it's expected to happen, and they're designed to mitigate it. Most home air conditioners AREN'T designed to deal with running a supercold evaporator with slow, humid air for hours and hours at a time, so they'll ice up if you aren't careful. My advice: if you're making your own thermostat and decide to run the blower at reduced speed, have it kick the speed up from 60% to 80% after 15-20 minutes, and have it kick the speed up to 100% after 40-60 minutes. The algorithm can definitely be improved upon, but this simple logic will generally be good enough to prevent coil-freezing if the system is working properly.
Also, note that contrary to marketing propaganda, a dual-stage compressor will NOT necessarily give you better EXTREME-humidity-removal than running a conventional single-stage compressor with the blower at reduced speed. As noted, latent heat removal uses a LOT of energy... if your goal is 72F @ 32% or less, running the compressor at low-speed might not actually get (or keep) the coil cold enough to SUSTAIN that kind of intense humidity-removal. If your system won't allow you to reduce the blower speed enough when the compressor is running at low speed to get the coil below 40F, you might very well find yourself having to run the compressor at regular speed and just cycle off the compressor and blower the same way you would with a single-stage system to achieve extreme dehumidification.
In any case, achieving extreme dehumidification with a central AC alone almost always requires the use of a homebrew thermostat and controller (Arduino, RasPi, ESP8266/ESP32, etc) and a lot of tweaking, because it's basically the HVAC equivalent of overclocking a PC. It works... but you're officially on your own, as far as the manufacturer is concerned. And your electric bill WILL reflect your extreme dehumidification habit. Operating your AC at 80% normal blower speed will probably increase your summer electric bill by at least 25-50% compared to what it would be if you endured the higher humidity. On the other hand, it's REALLY nice to enjoy a 72F 28% anti-sauna when it's 96F and 95% outside. ;-)
Also... to answer the original question, some manufacturers DO have add-on modules to dehumidify without cooling. For example, Lenox has a module that sits between the evaporator coil and air duct & can be switched in to use the waste heat from the evaporator coils warm the air after cooling it when operating in "dehumidification" mode. In a climate where your house would often be colder than 70 degrees even if you turned the AC off and left the windows closed, it might be worthwhile. In a climate like South Florida, it's probably unnecessary, and simply reducing the blower speed to 40-60% normal and running for 15-20 minutes per hour would probably be good enough to dehumidify without significantly overcooling the house.
How a dehumidifier works is basically the same as an air conditioner. Both remove heat from the air. Cooling the air causes excess moisture to condense onto the cooling (evaporator) coils which must then be drained away. A central air conditioner dumps the heat it removed from the air outside (via the condenser coils); a dehumidifier dumps the heat back into the air it just cooled.
To work as a dehumidifier only, your central air conditioner would need to have a second condenser coil installed above (downstream of) the evaporator coil, and have some means of redirecting the flow of refrigerant to either the normal (outdoor) coil or the indoor reheating coil. This would add extra cost and complexity, and reduce the overall efficiency and reliability of the system (more obstructions to airflow, more refrigerant plumbing, valving, etc.).
I guess it must be worth it since, as ThreePhaseEel comments, it is an option on some systems.