Anybody else feel like they're getting punished for having low ping/above average internet connection??

I'm fairly average at shooters, but I have played enough of them to know when TTK and TTD is way off. I consistently unload half a mag into enemies and get like 80 damage before instantly dying to what feels like three bullets that hit me instantly. All the while I see my bullets hitting the enemy as there's blood but the server is not registering it as damage.

I've seen a pattern among my friends: The better thei connection the worse the netcode issues are. I have 60+ fps (lowest settings on a mid PC) on a 1Gbit/s LAN connection, usually on a >20 ping. Anybody else feeling they're getting punished for having a good connection? Is there a workaround to improve the situation?