They don't show your history.
> the ad profile Google builds on you is probably more damaging to your privacy than a photo of the entire contents of your wallet.
I can take measures to prevent Google from linking together a full profile. It sucks that it's necessary, but once you log in it's effectively game over. And your payment info has enough stable identifiers that it's trivial to link you to pretty much anything else you've paid for.
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The core misconception here seems to be the idea that there is such a thing as a honest for-profit corporation.