It looks like Teamspeak covers the "group of friends who voice chat each other" use case (Discord DM groups) but not the "IRC replacement" use case (Discord servers). As far as I can tell, the licensing for Teamspeak 6 (the version that tries to be competitive with Discord) is set up such that anybody who joins the server (as opposed to anybody actively using it) uses up a slot, so the licensing fees for larger servers would be cost prohibitive. Additionally, the text chat functionality is way worse than on Discord. There's no way to just have a chat channel, you can only view and use the text chat when you're in a voice call in a voice channel.

Server admin can set the voice privileges on a channel basis, limiting effectively channels to text only.