Settings up new "servers" is trivially easy and can be done without payment. You can join any number of servers with same account and retain separation (i.e. other users can not see a list of servers you are on). You can change your nickname on server-by-server basis. "Everyone" is already on Discord and by everyone here I mean every gaming community and many tech communities.

For TeamSpeak, Ventrilo, and Mumble (which were the big 3 in my youth at least) you have to have different clients, you have to pay for servers, and the chat support is very rudimentary and bad. Channels aren't as easy to create and admin. Lastly they don't support inlined links/images or emojis. Which makes them just as user friendly as IRC.

Discord took what was good about Slack's UI and added on top good VoIP. It might not be perfect but it quite literally covers most what anyone could want and it scales really well. To beat it you must have 100% feature coverage + another killed feature. First part probably isn't that hard, but the second is. There needs to be a reason to install yet another communication program on your PC/tablet/phone because all of the communities wont just uproot and leave to a new platform over night.

How will they be able to pay the bills with this approach?

Datamining the users and then selling the data. Also probably have some governments paying them to spy on certain users.

How does Facebook, Twitter, Reddit, etc finance themselves? Selling data and also having subscriptions. If you pay $5/mo you get higher quality video streaming and you can use custom emojis cross the servers you visit.

I think The issue with teamspeak and Ventrilo were...cost. Kids couldn't afford hosting a server.

Additionally, it was stupid easy to evade bans on those platforms and troll for hours if Admins weren't on.

The value of a network is exponential in the number of users/connections, not in the technical features available. See Voat vs Parler or old Digg vs old Reddit.