ISPs can presumably correlate the Google query string with the request following the response to the goto and so make a search index? I guess they would charge too much.
Do any large ISPs use visit data to feed into a search index?
Do any large ISPs use visit data to feed into a search index?
There's even a reverse pointer query that can be made to get a domain to IP from a legacy ARPA TLD, although it isn't 100% robust.