How dimmers work
It sounds like you have some very common misconceptions of how dimmers work. The usual assumption is they reduce the voltage; however that would require either a) a Variac (about a 30 pound transformer bigger than a soda can), or b) a large power resistor about the size of a shoe box, that makes lots and lots of heat.
That's not how it works at all. Actually, the dimmer supplies full voltage, but only part of the time. It waits until a certain point in the AC cycle, then turns the power on full. As the AC voltage follows the sinewave to zero, the switch shuts off automatically. Then, the dimmer waits a period and turns it on again. So the light only sees part of the sinewave. This scheme is done to keep the dimmer lightweight, small and cheap, so it's built around a 30 cent triac instead of a $40 transformer.
Motor speed control is a different kettle of fish
You can see where that would make a motor very, very angry. Further, many motors are designed to go one speed: the speed of the AC frequency, and to regulate their speed you need a Variable Frequency Drive, a sophisticated piece of electronics. So trimming voltage but keeping frequency just imbalances the motor and makes it hot and inefficient.
There are other schemes to control other types of motors, but none of them are anything like dimming.
So yes. Dimmers are for lights; motor speed controllers are for motors. Hence the names of the devices.
You can use any UL-listed control scheme that works
You are perfectly welcome to have two switches side by side; one being a dimmer and the other being a fan speed controller, each feeding its respective devices. That would, obviously, require a 2-gang box and some more cabling fished in the walls, but it's straightforward work for any competent electrician of the "specialize in fishing cables through walls" variety. That electrician could also make sure to install a fan-rated junction box which is capable of bearing the extreme vibration loads that will pull the nails out of a normal box, or metal-fatigue it.
Another option, these days, is to hardwire hot to the ceiling, and use "smart" fan and light controllers to respond to a smart switch. However, this setup must retain what every room in America has: a light switch in the usual location that a complete novice can turn on. That is to benefit guests, particularly EMTs, cops and firemen who need lights turned on fast to intubate you, clear the room, etc. It can be a smart switch; it just has to work.