If you were to pay, then you'd have to enable Google cookies to know that you've made the payment. If you enable Google cookies for those sites then you don't have to deal with the reCaptcha (as much).
I'm not a huge privacy freak - I have the default cookie settings on all my browsers and I'm signed into multiple Google accounts. They know who I am. I can only suspect my adblocker could be blocking something there, but other than that I should be about a regular of a user as they come.