Not being able to cook would lead to having cholent only if someone wanted to eat a hot meal. It's the additional fact that fire can't be lit and the desire to counter the mistaken Tzaduki understanding that fire can't be left lit at all which motivated the practice of leaving food to cook all night.

I found interesting that in the question itself they specifically mentioned that the prohibition in the verse caused them to leave the food on to cook overnight, and the first answer offered was "what is cooking?" - the question itself built that in as allowed (in certain ways at least, but with that specific word)