and that's exactly it. putting something in your music library is a hugely more visible and tangible thing than all the nebulous privacy concerns the internet wants me to be afraid of. nobody gives a shit if google or apple or facebook or whoever else introduces some techical measure that could be used for nefarious things. they only care if that api is actually used for nefarious things. as long as the argument is "well if google implements X, then it would potentially allow them to do Y*, that's a failing argument.
like it or not, people actually do trust the big tech companies. as long as they aren't actively abusing that trust in ways that people care about, things like "google wants to know if you're a real person or a bot" aren't going to cause a whole lot of outrage. most people can understand that letting fake people pretend to be real is bad, and that preventing that is probably a good thing.