CjR,
Do the tires cut in while going straight (read - sinking in) or only when turning (digging when pivoting)?
If when going straight, I see no problem other than you'll probably want to keep them narrower than the mower itself so you can pivot around trees and stuff.
If the latter (when turning), this can be stopped by assuring both tires are moving when doing any pivoting or turning. If you want to do a U-turn, don't pivot on a single tire. You need one tire going backwards, the other forward.