The initial positioning of both parties and the terrain features are all arbitrarily decided by the DM anyway. To me, all relevant questions have always been pretty easy to answer without miniatures, unless the number of participants exceeds a certain threshold. I don't see that everyone needs to visualize the space effectively, as long as the DM can.
Sure they do. It still usually boils down to "who can I attack, and when?"Really? Your players never execute an ambush, or get to fight any battle where the terrain and distance get to factor into their tactics?
I think the term "theater of the mind" takes that into account. The DM describes the space, the players visualize it. They either determine their course of action from the initial description, or ask questions and then decide what they want to do. The battlemap can be helpful if the situation is too complex for people to visualize, but that's quite a high bar.How can the players make effective decisions without visualizing the space effectively? I'm not saying that minis are required for this to happen but if it doesn't in SOME form the players are simply flailing around blindly engaged in a furious exchange of maths, without any reasonable way to exert influence over the situation.