Push to talk is most certainly not obsolete. I (and many gamers I know) use push to talk for the privacy of being able to choose when your microphone is activated.
Its even more useful in competitive gaming and/or streaming where many want to chose what to say to their team/friends and themselves/the stream.
Also helps a lot in large communities. There will always be people that are nice and you like to have around, but are a bit "louder" during gaming sessions. We were really successful by teaching them to not hit the PTT-button when they need to drop their load of frustration.
The gaming community that I am a part of that uses Discord holds a weekly big gaming session where almost everyone attends at the same time. It occurs around dinner time on the west coast, so some of our west coast members will be having dinner between rounds. Push to talk allows them to talk between bites without all of us getting the smacking sounds of chewing and eating in our ears.
Push to Talk is necessary when you regularly have 200+ people, sometimes 800 people in the same channel. We don't use discord for comms because it doesn't support shout + channel hierarchies unlike mumble. Discord is still useful for pings, as their mobile app w/ push notifications are very helpful.
Definitely not. If you have been in a channel with 25+ people for a raid or large event (exactly the type of gaming community Discord caters to) then you should know push-to-talk is absolutely required and you will often be kicked if you don't use it.
Yeah - there are games for which I will use voice activation, like PUBG (where I do not have the mental availability to hit a PTT key), but for Overwatch I started with PTT with one of the thumb buttons on my mouse and I still do it.
That said, I use a for-realsies dynamic microphone with tons of off-axis rejection and a wall-mounted arm (I play games in my office/recording space, that's the engineer station mic). So I probably could use voice detection and be fine. But habits die hard.