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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.

Omg, thank you. Somehow I'd missed that setting.

Check out BetterTouchTool if customization is holding you back.

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)