Unless you're referring to worries about giving out your payment information to "random sites"? If so, that's dumb because it's 2019 and there are tons of dedicated secure payment processors out there. Very few companies would even be willing to process payments themselves.
Any effort to take power away from Google's iron grip on the internet is good unless you're a Google employee or shareholder.
Perhaps they do, but the headline "X leaked data of millions of users" is more likely for X=Tinder than for X=Google, if you ask me.
The only thing that the actual vendor should see is a purchase from "a Discover customer."
Hell, for most online transactions I would like to proxy the whole thing. If I could give money to someone to buy things on my bealf and put their name, address, and shipping info instead of mine and then ship it to me I absolutely would every single time.
Many payments on the web are done by handing over payment card details and trusting the merchant to bill the correct amount.
The alternative is to use a middle-man like PayPal.
It's absurd that the banks and credit card companies haven't come up with a better solution than handing over your card details and taking it on trust, but here we are, and online sales are doing fine.
It's a regular occurrence for companies of all sizes to fail to protect customers' payment card information. For some reason, no-one talks about how preposterous is it that we still handle many online payments through total trust.
Little comfort knowing your card details will eventually expire, especially considering that they no longer really do [0]
As you say, far better to go the PayPal route, despite their considerable problems [1]
[0] https://twocents.lifehacker.com/some-bill-providers-will-aut...
Does privacy not concern you?
Granted, Google probably is quite supportive of users vs app vendors, but the risk of losing their Google account is gigantic for many users, and there's no useful way to appeal (unless you happen to be in luck, your complaint goes viral and somebody from Google manually intervenes).