How private are things like matrix if you DON'T host your own server?

Since matrix can be self hosted, a lot of the privacy discussion I can see online mainly mentions that as a selling point, and while it IS a good selling point, that's a lot of extra consideration most people don't want to deal with. So, without hosting a custom anything, how private/freedom respecting/etc. is Matrix as a general system, and do any clients do anything special as extra considerations.

(alternatively, if there is another privacy respecting discord-esque communication method that …

don host matrix own privacy server things