I come from mainly playing King Of War (2nd Ed was the last time I played that though) for large scale games and with that one side fights while the other does nothing - literally the attacking side does all the rolling. This was one of things that I wasn't keen on as I like interacting with the other player which is what lead to the system I have now.
So to answer the question, no we've never had a stalemate. You might send a strong unit up the middle which can take a bit of flak while get your faster units either up the flanks or, if you have them, flying over the top while you archers/artillery soften up the front units. Or you might send up a 'soft' unit up first so the opponent has to either deal with them, allowing you more elite units to jump on them, or hold back but even a 'soft' unit can cause damage and force a morale test.