I think maybe we're envisaging different things here. I don't make whole heaps of monsters immune to being stunned, just more than the Monster Manual does. Constructs, basically. Unless your campaign is filled with constructs that's not a major problem. You just occasionally come across things your superpower doesn't work on. The whole party finds themselves in similar situations at some point.Stunning Fist is central to the Monks Oomph from 5th level onwards. If you make a whole heap of monsters immune to Stun, you're totally nerfing the Monk class.
It would be like making a whole heap of monsters immune to Radiant damage. Your Paladin players will hate you.