The game clearly ought to have better mod management tools, but man you are switching mods way too much. I never switch mods anymore unless I have to. The best mods are on my arena team, and they stay there. Rancor is easy, there is no reason to switch mods for it. HAAT, we had people switching mods for the first few failed attempts and the first few successful ones, but once it's on farm, that's just unnecessary. My extra TB teams are modded with whatever I had lying around - for the waves I can't complete, lack of gear on those characters is the deciding factor, and in most cases, me getting an extra wave isn't going to make a difference in our final star count. It's just not worth the hassle and cost.
If an event comes around that I can't finish without moving mods, I will move them, but most events can be done just fine with whatever mods I had lying around (and probably stuck on those characters back when I last needed them). Maybe every other month I might need to switch mods to get through an event.
