If they actually wanted to improve it, the key would be to move away from the advertising funded model - as Larry Page and Sergey Brin warned in 1998 "advertising funded search engines will be inherently biased towards the advertisers and away from the needs of the consumers"[0]. Personally I think they could at least pay running costs with a paid support model - it might not earn as much money as advertising, but as a gateway to the internet and other Google services it could still be very valuable to both Google and their users.
[0] "The Anatomy of a Large-Scale Hypertextual Web Search Engine", Computer Networks, vol. 30 (1998), pp. 107-117, (noting that the quote is in Appendix A which seems to be missing from some more recent online versions).