I agree about the why? question. Unless you put casters with the little lock mechanisms on them it would be really unstable when playing. Even things (carts, dolly's) that normally have that type usually have two fixed direction casters and two swivels, but it would be a real hastle to get a foot under there to lock it down every time you move it. That would be the reason for casters to begin with. There are probably hundreds of ways to mount and reinforce them that would work if you are really comitted to the idea. Would particle by itself hold them, probably, but not well, and not over time. Reinforcing it with any of the ideas mentioned would probably work better. Overall cab weight is another factor.
Just to throw another idea at you: If you want it easily movable and stable why not use two standard corner mounted upright cab wheels mounted (vertical) inside on one end and 4 leg levelers underneath. By mounting them to the inside they would be just barely visible. Make sure you build it stable enough to pick up the other end and you could wheel that sucker anywhere you want and set it down nice and solid in place again. Just an idea.