All this is true, and yet when I use Google Chrome's search autocomplete (which is partly server-side and partly client-side), it will usually fill in exactly the query that will get me what I want (rather than what query I think will get me what I want) before I even start typing it, using some combination of searches I've done before and the indexed text of open Chrome tabs.

Google by itself isn't very good, but Googling from the Google Chrome address bar these days is something else.