This actually does seem to be bad intuition to me, because your intuitive explanation isn't being expressed in terms of strategies. You wouldn't want to "attack this frontline unit" but would want to have a probability distribution over your potential options. This is similar how you wouldn't want to "play rock" in RPS, but would instead want to play {R: 1/3, P: 1/3, S: 1/3}.
In a certain sense the thing that is "different" about imperfect information is that you shouldn't play as if you are making only one decision. You should play as if you are in multiple different game states at the same time.
FWIW, I don't think detracts from your point about it being possible to simplify the game, just your reasoning explaining the "why" we ought to seems off to me.
My point is that your decision to attack is one that takes 3-5 turns with no meaningful possible positional maneuvering. So a game may have 200 turns but many fewer "decisions". There's not much "area control" like in many other strategic boardgames. It's more bluffing about your original setup choices. Every battle is reduced to a bet of whether your unit is higher or not and if it is, well you don't have a lot of agency on that. Especially if attacking.
Without perfect information, the number of states is still mostly a red herring, because the differences between the states are immaterial. The moves aren't super important. If you decide to move frontline unit A against the frontline unit on the opposite side of the field, there may be several moves between that but you've only made one noteworthy decision. Could be bad intuition. I think a more abstract model here would do better and be far simpler with some minor tactical move prioritization or whatever.