>The problem imho isn't GTM (Google Tagmanager) running as proxy. This would (or at least could) be a data privacy win if done ethically. At least under one imho essential condition: I could be able to run the proxy on any infrastructure that I like. Not only one Google's cloud offering.

Yup that is where rubber meets the road. Would like to offer google as little data as possible. And use as little google products as possible on the web and internet.