I think that a lot of this sounds like it would need sophisticated machine learning/data mining algorithms. The reason this doesn't exist is probably because it's difficult to develop these algorithms without having huge datasets and user feedback which comes from, you guessed it, companies having your data. I'm not saying it's impossible to do, but it's definitely more difficult to adapt existing datasets to your software than to collect them yourself, in a format that you dictate. Maybe in a decade.
It's true that your computer will not be processing as much information as big as datacenters. But the debate of how relevant to you the results will be could be solved by tweaking or updating the algorithm. Yes it will take time to find the best solution, but remember, this is just one feature of your machine. It could be solving other problems that have nothing to do with search. It all depends on what you want the computer to do for you.