We thought about listening for AVRCP key events to detect when a certain button was pressed and released -- probably play/pause, which seems to be the most prominent button on most headsets. It would have been hacky, though, and we ran into several problems. For one thing, a lot of headsets power off if the play/pause button is held down for several seconds.
We also had concerns about audio quality with third party headsets, especially those which didn't support modern versions of SCO (which introduced new codecs with 16khz support and other improvements), or with poor antennas leading to high packet loss (SCO is a lossy protocol, so we still get some speech and attempt to translate it, but accuracy suffers). We were concerned that all accuracy problems would make Google Translate look bad, even if the headset was to blame.
What about an app that you interact with rather than something physical on the headphones? Considering the phone is required, anyway...
The problem that the Pixel Buds integration aims to solve is that it gets cumbersome for two people to hand a phone back and forth. With the new UX, one person can use the phone while the other uses Pixel Buds for the duration of the conversation.