From a technical standpoint it’s definately possible but it’s virtually useless because consoles restrict input movement to steady actions. To get an idea of this, I recommend you play the release day version of Halo2PC, it gives the best approximation to what using mouse/keyboard on a console would be like because they didn’t properly port the controls. After 5 minutes you’ll be acting like that angry German kid. Unlike in normal FPS where you can zip around and shoot, in consoles the action has to be smooth and the “zip” action only registers as a small amount of movement.
IMO, there are two reasons why MS hasn’t released the newer Halo games on PC. First and most obvious is because Halo2 Vista flopped hard. Halo2 was a major failure because it wasn’t properly ported and was released months before it was ready, mainly because MS wanted it to be one of the flagship titles in the Games for Windows Live program. Reason numero dos is that MS would like to keep it as an exclusive XBOX360 title, if at all possible.
The general consensus from google is that MS assumes PC sales will be low so in their minds why bother. This overall lack of intelligence is why Microsoft’s Home Entertainment division has yet to turn a profit.