1) Ads. They need to be able to log your hits so they can charge advertisers money.
2) Security. Not logging visits means they wouldn't be able to trace back suspicious activity, etc. If you somehow managed to hack them through their private web search page, there wouldn't be any traces of you.
There aren't many good reasons for this anyway. It wouldn't make your searches anonymous to anyone but Google. Your ISP would still have a complete record of everything you've done. And since Google doesn't really see themselves as someone you need to be protected from, what is the point?
They would gain more users than they would lose revenue by implementing an easy to use and east-to-switch-to private mode. You know, for when I'm searching for horse porn, or whatever it is that I care if Google knows I'm looking at.