You play an FPS and everyone uses the meta gun at the time

This is why I miss arena shooters (Quake, Unreal Tournament, Halo, etc.) being in vogue. There are no loadouts, no inherent differences between players, you're all equal, and any weapons, ammo, grenades, powerups, vehicles, whatever, must be picked up from the map itself. This map doesn't have a lightning gun/rocket launcher/banshee? Well tough shit, you're going to have to do without.

These are games where you must fight with whatever comes to hand, no matter how much you dislike it, and that leaves almost no space for a meta. The closest thing that can exist is a general consensus of "for this situation, these are the weapons you want to have, and these are the weapons you really do not want to be in this situation with".