The discord servers my friends and I use are just for shit posting and using voice among like 10 of us. If it becomes annoying we can move to the next thing. We're all millennials. We can run whatever server if needed it's not a big deal.

If you meet somebody mid match in a game like Valorant or Overwatch, it's simple to give them a username and they can add you and you then choose to group voice call vs inviting them to a private server, especially before you know them very well.

Teamspeak, as far as I know, doesn't have a way to solve this.