Basically there are two log files kept:
- One for up to 48 hours which contains IP addresses, which is used for handling abuse.
- One is permanent which doesn't contain any personal identifying information (eg IP addresses), which is used for things like internal performance monitoring, load testing, and tracking frequency of longer term abuse etc.
Google provides Google public DNS because if you see the internet as being slow because of poor DNS performance, then you don't use websearch as much. Google doesn't need to use Google Public DNS to track users, and would rather not have the information (as it makes it available for government requests etc which are a major pain to deal with). But running a large scale recursive DNS server tends to attract a _lot_ of abuse, both intentional, and unintentional as I'm sure 9.9.9.9 and 1.1.1.1 are discovering.
Google provides Google Public DNS because a lot of ISPs provide extremely poor default recursive nameservers (having tiny caches, dropping queries due to overload, not implementing IPv6, DNSSEC validation, EDNS0 payload size, or other important modern DNS features. Some ISPs also hijack domains for their own purposes, or "stretching" DNS TTLs etc) so providing a better alternative to improve overall Internet use is clearly in Google's best interest.
Having other public resolvers, with different trade offs is clearly better for everyone, including Google as long as they are reliable, trustworthy, and provide low latency responses.
Good luck to everyone who's joining in the fun of running a planet scale recursive DNS server.
(Disclaimer: I have previously worked on Google Public DNS, but no longer do)