That is a reasonable consideration, but Google is very specific about how they use and retain data collected by Google Public DNS. Assuming they are not lying, I don't think it's a significant concern. (Admittedly, their policy is not as good as Cloudflare's "no IP logging" policy.)
https://developers.google.com/speed/public-dns/privacy
TL;DR: Logs with IP addresses are deleted within 48 hours; permanent logs keep city-level location data, but no personally identifiable information. "We don't correlate or combine information from our temporary or permanent logs with any personal information that you have provided Google for other services."
Hahahha, and then he said "Then switch ISPs", like we have more than one high speed choice where we live".
Due to laws designed for more broadband competition, I've got over 6 providers to choose from here in Germany.