I would have a problem with that, because for a search engine to know me well enough to know what I actually want despite what I typed in it would have to know a lot of information about me I wouldn't trust the company behind it with.
I spend most of my browsing time in a browser configured to clear cookies, cache, and history on exit.
I'm not sure why most people are okay with companies gathering tons of data about them and trying to use it to manipulate them into buying products they don't actually want or need (among other uses), but I'm not one of them.
Now if I could only get a search engine to not ignore query terms because it thinks it knows what I want better than I do, I'd be even happier.