> You are basically using Google by proxy unless you use a truly independent browser engine

This conclusion doesn't follow your premise. Google has to pay because if Mozilla dies, so does the claim of any real competition on the browser engine market. So everyone agrees Firefox's engine is truly independent. Google pays so Firefox users don't use anything that has to do with Google.

If you think about it, the only real way to not hurt Google is for Firefox to stop existing. Chrome would end up being spun off from Google.