First, you are being overly critical. Automatic (forced) sign-in is actually useful. Second, why do you call leaving the "only" recourse? As if it's something completely horrid that you would never ever do freely. Leaving is a completely fine path to take.

With webRequest, Google is "just" testing the waters. Just like with the forced sign-in, they will back down when they see the backlash.

Based only on Google's description, they seem to have a valid reason to remove (even though they say "deprecate", they mean remove) the offending API. However, there's zero chance they can get away with this. For what reason I'm not sure, market share of Chrome is very important to them. So they'll have to keep it or implement some new, acceptable method.