Why can't you install Photosynth on your PC? I don't understand.
In answer to why Photosynth doesn't perform the computer vision on Microsoft servers, the answer is that, as you noted, the computing power can be significant for large synths.
Watch this video to have some of the Photosynth team explain for themselves exactly why they do it this way:
One of the many reasons why synths are upload only is because they can be quite large if there are many images or large images in them (or both). Because of this, they are automatically put where anyone can get them and the parts that someone wants to look at are streamed to them so they don't have to download the whole thing before looking.
Both Google and Bing are using Photosynth-like image matching on databases of photos - Google with Panoramio + Picasa geotagged photos and Bing with Flickr Creative-Commons geotagged photos.