Not sure if it's helpful for you but you can customize the behavior by going to your System Prefs > keyboard settings and toggling "Touch bar shows:".
I did this on like day 2 of having my MBP for what sounds like the same reason you want to. The setting I have turned on is "Expanded control strip" and I never see any application-specific controls, only volume, brightness, etc.
FYI you can customize it, and force it to always display certain controls.
I had the exact same frustrations as you. Took me 10 mins digging into settings to figure it out. Now I have my touchbar constantly displaying all of the controls that are buttons on the Air (ie a completely over-engineered solution to get the same result)
If it was more customisable I wouldn't mind it, but the apparant inability to force it to show me the things I actually want is annoying.
I can imagine there are some people for whom the application specific buttons are useful, but for me they are not worth it for what they displace.