Even back when the lobbies were p2p there was still infrastructure on the developer side to handle the matchmaking, stats and progression. I’m sure the load is much less but the multiplayer experience isn’t as good. It would also be pretty demanding for some games that have huge lobbies like battlefield

If you get all the way into the game then go offline I believe it still works. I’ll have to test again but I do recall being able to play without internet after resuming from sleep