Find out What's Going On
Dedicated servers cost money, but aren't the players those who would finance these? Overkill could gladly step out of it. We wouldn't need official servers. We will just set up our own. People have been doing that in games made with the Source and Unreal engines for decades. Even games long abandoned still seem to be alive because there are fans who are willing to pay for their own dedicated servers.
Games running with peer-to-peer seem to die more quickly, as there is zero transparency as to how the gamer population looks like, and there is no way of drawing people in by advertising servers (obviously, because they don't exist, only vague and temporary lobbies). If I want to get people come play on a dedicated server I can join one, go afk, check back once in a while and hope for some to come, maybe invite friends or whatever. They can use powerful server browsers to quickly search for this server, and join if they like whenver their time allows it. You don't have any such control in games running with peer-to-peer and random matchmaking. It's all hastily made up, and hastily dropped as well.
Dedicated servers probably are better to administrate too. I guess anti-cheating measures are working better on them too. And there is the freedom of modding and using plugins. Anyone who has played some Source or Unreal games will have played on modded servers, and have experienced interesting altered versions of their games. Not all modding is good and makes sense, but it's still something that can keep things fresh.