I've never used the CCI milspec primers and I've fired thousands of rounds through several semi's with military-style floating firing pins. I use regular CCI and Winchester primers.
That's not to say I think they're never required; I understand different rifles (even of the same make) can respond quite differently. I check my own rifles and have never owned one that left more than the smallest, almost invisible dimple in the primer when chambered. If I bought a rifle in the future that, when tested with a primed case with bullet but no powder, left a significant dimple, I would seriously consider ordering some CCI milspec primers.
I know several people who have "sticky" feeling firing pins in their semi's (SKS', Norc M14's); a couple of which have caused slam fires with Commie surplus ammo. Their rifles leave significant dimples in the primers when chambered; larger than I'd be comfortable with as per what burnt_servo said.