The fact the Battle of Cheron is mentioned offhand on a screen in a single episode of Enterprise is not in any sense a statement that only a single battle was fought in a four-year long war. It is patently ludicrous to assert that it is. Enterprise not featuring atomic weaponry can most easily be explained by the need to produce larger volumes of weapons more cheapy. Your point about the colonies is nonsensical - there is absolutely nothing in The Original Series or Discovery which indicates colonies were not attacked in a war that took place a century beforehand.
I think my point is: let's not read into existence speculation meant to make this all make sense. I agree that there likely has to be one other battle at least, but we just don't know what happened and making decisions on incorrect info is always a risk.