I can actually imagine a lot of users liking that - many people I've seen using a browser will just type stuff in to Google's homepage search box and then follow links. The classic example, yes I've seen it, is people typing Hotmail/Live/Outlook in to Google and then following the link rather than typing in the address [my 8yo did this recently for another site].
For many-many users the web entry point is the search engine they use as their homepage, that is "the internet" for them. This was the paradigm that AOL developed and there are vast swathes of users that cut their teeth on AOL.
I think that's an ok thing. I used to scoff at this sort of behavior but no longer - users who do this are just doing the same thing I do in the address bar, except they're taking up a whole page and an extra click. The address bar is probably too ephemeral and hard to understand.
It's probably a good hint that browsers could find success at imitating a similar search interface in the new page/new tab UI. Offer a clean page with a text search field, with very fast results that have good context.
Chrome and FF have a "View History" page with search, but it seems to be fixed by date and with no way to sort for relevance. IE doesn't appear to have a history search (I think this is baked into Windows search instead?).
For many-many users the web entry point is the search engine they use as their homepage, that is "the internet" for them. This was the paradigm that AOL developed and there are vast swathes of users that cut their teeth on AOL.