All this "glorified medicine cabinet" talk is a little bit uncalled for. These are actually called "Structured Media Enclosures" by the manufacturers, and for many (most or virtually all) home networking and video distribution installations they're adequate. They do come in different sizes, too.
And, you get your own Ethernet punchdown blocks and install them in the cabinet.
If your cable modem and your ethernet switch are wall-mountable, then you can mount them directly to the back of the cabinet. That's one of the purposes of all those handy little holes in the walls of the cabinet.
Here's a picture from Leviton of one of these things populated with more gear. The item labeled #9 in the photo is an Arris (Motorola) cable modem.
Now, having said all that, the picture of the panel I included here is about as crowded as I'd want one to be, and I would worry a little bit about heat buildup. Although none of the devices pictured use enough power to require active cooling.
Also, there's no way I'd put my WiFi access point in a metal box, unless I was mounting it in a sensitive location or exposed to the elements and I had it connected to an external antenna outside the metal box. In the house, I'd run Ethernet cable to one or two appropriate spots on the ceiling and mount the right kind of PoE access point there. Perhaps two of them in different parts of the house.
The housing of a 16-port switch won't fit in this box, and the heat buildup from many 16-port switches would be too much for such a small enclosure, although a couple of low power 8-port switches clearly will work.
Personally, if I were building a new house, I'd install the biggest enclosure I could get my hands on, or more likely, I'd just build an actual closet with a 19" rack and an exhaust vent I could attach a thermostat-controlled fan to, and pull all the cables to that point.