Those who know me know that I'm not in favour of most Google stuff. I struggled a LOT with my move from Apple to Android because I don't trust Google at all. Banking with Google, therefore, is off the table for me. But, perhaps not for the reasons you'd think.
I definitely do have a concern with Google being involved in my financial affairs, but I use Google Pay to tap. Albeit, I do it out of a "burner" bank account that is not at my main bank, and that bank account only exists to transfer spending money into so I can tap to pay. My main bank handles my payroll deposits, retirement and brokerage accounts. I don't like Google handling my payments, but I can accept it by limiting Google's visibility into my financial affairs to only what I buy and not how much I get paid and save, what stocks I move, etc.
But there's another reason I don't see myself opening up more of my financial affairs to Google. And that's because of the other reason I don't trust Google which is it can't be counted on. Google routinely kills off projects that people rely on. Google Plus, Keep, Buzz, Reader...on and on. Google doesn't give a second thought to closing stuff down even if it has a huge user base and I don't feel like having my financial works go into limbo if Google decides to do so.
There's also a deep concern about getting locked out of the Google ecosystem. That happens. A lot. Google it. People who rely on Google too much can have their entire lives shut down by running afoul of Google and being locked out of their account.
It's an easy decision for me because there's really no advantage to using Google for anything other than tap. Perhaps that's because of the robust nationwide Interac system we have in Canada that allows anyone to send money to anyone else with a bank account already. I don't know if the US has something like that, and if not, maybe that's why Google sees a market there.