Yes but the base bandwidth used by games is actually quite small. Let's say (overestimate) that you have 10 input events per second that need to be broadcast. That's going to take maybe 100 bytes, tops. All the other players are receiving events from 10 people, so 1k each. Times 10 players. 10k per second. My bandwidth is 400x that.
Of course, that's not actually how most client-server games work. Rather, they send you updates just about the objects you can see. Which probably takes significantly more bandwidth than just broadcasting keypresses, but not 400x more bandwidth.
We've had times when all 12 of us joined a public TF2 server, and it worked out just fine.
50ms latency is within the range that games can hide using client-side prediction, though I think my connection usually gets better pings than that.