I wired our bonus room to include a 14/3 wire from switch to fixture with the assumption that I could hook up an "infinite" speed control fan. Come to find out that most if not all ceiling fans do not recommend this approach because it could burn out the motor or is otherwise a fire hazard? I don't get this. Our previous home had a variable speed dial to control the speed and I was hoping not to have to use those stupid remotes that run out of batteries or otherwise get lost. Certainly I could just replace the switch with a pole one and use a remote, but I was just wondering if I should proceed with my original idea or just default to the remote option?
You should not use a dimmer that is designed to control lighting, as that can cause problems. Instead, you should use a fan speed control device, that is specifically designed to control a ceiling fan. You'll also want to make sure the control you're using, is rated for the maximum current draw of the fan you're using.
There's no real difference between the in wall speed control, and a remote speed control module. Both devices control the speed of the fan, external to the fan itself. The only difference is where the device is located (wall box vs. ceiling box).