Every internet search involves a person who usually has a very clear idea of what they want to see when they undertake a search. They'll probably type two or three keywords to try to describe what they're looking for.
So given the limitations imposed on the SEs, by us mortals, it could be argued that they - more specifically Google - perform an amazing job... maybe it is we, that needs to catch up; could you do a better job, manually? ;)
But if you ask them, they can tell you all kinds of other information about what page they are looking for, including massively complex associations between different words and topics.
And this is where the "advanced" operators come into play: daterange, subtractors and the like, for instance. I think we're now talking about the longtail and corpuses, and stuff.
Again, though, human language itself is limiting - some languages more so than others.
Ask five people to describe the same room in three words - You get the picture, I'm sure.