This is a good point as well. Ultimately any search engine has user IP address though, modulo VPN and similar technologies. For a regular user who signs into G

This is a good point as well. Ultimately any search engine has user IP address though, modulo VPN and similar technologies. For a regular user who signs into Google to use Gmail, they'll be searching while signed in anyway - no real loss of privacy, and arguably much gained by not broadcasting anything into the adtech data pools. For a very privacy conscious user who wants to be anonymous and is already taking steps like using VPNs, there is a loss in privacy due to payment info being attached. (You could argue Google accounts could be pseudo anonymous, but for most users they're anything but - location data, history, emails and search queries make them totally identified). There are technical solutions to avoid the payment linking issue (cash in envelope, selling gift cards via retail, etc), or through using blind signature schemes to separate payment from usage. The user experience of these options is likely to be far more complex, with people losing access and customer service fiascos with people being unable to prove they signed up before etc.