I know there is a limit to the number of times you can upgrade a mine (L20) and hospitals (changes with the hospital, but usually ranges from L1 to L7), but I've never upgraded an army camp so far that it maxes out. Is there ever a max? Is it ever advantageous to do it?

There is a max. You can easily hit the max when you play long challenge levels (with auto-upgrade army camp on of course).

Is it ever advantageous to do it?

Depends on what your goal of playing idle is. If it's for getting AP and clearing levels fast, then no. If it's for doing random cool and fun stuff, the yes it's advantageous because it brings you joy.

thanks. I guess I've just never upgraded that much. usually I find that by the end of the level, my hospitals are more helpful. I appreciate the response

I've had levels where I only had one territory left, but I wait a week or so before finishing and going on to the next level. During that period with cash accumulating but nothing to spend it on, I've tried upgrading an army camp to it's limit, but was never able to do it. so it's not likelu

Edited 9/8/2021 23:32:27

no reason to upgrade army camps too much.
at the end stages of the level army camps have almost no impact on the progress.
Also spending XXB money to increase your army production by 1K or so is a bad investment