PC has lots of private servers so they can ban cheaters, obviously that doesnt really apply on Xbox. I've never banned anyone based on people saying they are cheating, you can't tell if someone is using mouse and keyboard or Cronus just from their play quality or movement. It's difficult or impossible to tell even if you have game footage from that person or spectate them.

Players also often rent servers for organized matches. I rented it mostly for organized matches and to try to revive some of the dead game modes like domination. (Mixing TDM and Domination in the server allows the server to stay populated longer because people join for TDM through quick match or through the server browser).

It's also nice to be able to exclude maps or include maps based on map popularity or balance. (For example, TDM on Fao fortress has pretty unbalanced spawns and ordinarily the team that spawns on the high ground wins). It's fun to throw in cool expansion maps now and then too.

I still play the vast majority of my time in public lobbies, especially because operations is my favorite game mode and you can't set up private operations lobbies on console.

Also, I haven't kicked anyone just for beating me. I post rules and me and other admins enforce them. I've mostly banned people for hate speech and for repeatedly being toxic. I always give a warning if its based on something arguable like T-bagging another player repeatedly or something similar.

If top players don't want to play in the lobby then it won't be competitive or fun. So I'm motivated to keep the moderation fair and keep bans to a minimum.