AFAIK Ventrilo, TeamSpeak, and Mumble each support this

It's definitely common in gaming-focused apps, but not in the general or business focused apps like Skype, Slack, Teams, etc.

We use Teams on our team, and my current PTT technique is to Ctrl+Shift+M to unmute and mute every time. Très annoying.

Not to mention that often the mute button in many of these apps needs to execute hideous amounts of WebRTC-related Javascript in Electron, delaying your mute significantly. Signalling the CoreAudio OS system directly as Shush does is the right layer for the job.

IIRC even Skype has that option. Can you not bind this directly in Windows/macOS?

Skype only has "push to mute."