Yeah I also find it really weird that push to talk only ever surfaces in gaming focused voice chat. It's useful for any situation with more than a couple of people, especially when they're typing while on the call.
I remember during my days of wow raiding hearing someone else's background or breathing noise during the raid was not acceptable.
That doesn't work well for gamers, for obvious reasons.
NVIDIA Broadcast (Previously called RTX Voice) is a godsend for those scenarios.
If you haven't seen it, it's worth checking out. It is absolutely magical. https://youtu.be/uWUHkCgslNE
Sadly, AFAIK, it does require an NVIDIA GPU, but it doesn't need an RTX card. I used it on my GTX 1070 and it worked wonderfully.
What's really amazing about it is that you can use it to filter incoming voice audio, so if you have someone in your channel that has tons of background noise or breathing, you can filter it out on your own side.