Yes, you need to run the service somewhere. But anyone can do so (Foss).
With discord my experience is limited but I currently understand it's a service model so you're dependant on a company, which can pull the same sh*t teamspeak did at any time.
Not needing any technical knowledge just means someone else is running it, possibly being able to lock you in. And in the case of discord, you already are locked in and have to accept whatever they think up.