There is no problem with the ajax postbacks that navigate the folders.
The problem is full postback is required for a file upload. If the upload could be done in an ajax postback there would be no problem, but since it requires a full postback and we want to get out of full postback after the postback logic completes we do a redirect and this is seen as a brand new get request so we lose any state that was previously maintained by using ajax postbacks.
Content features like the shared files module also have to behave well on pages that include other modules, so its not really feasible to use url paramters for folders or changing the url in ways that may affect other items on the page. For example what if you have 2 instances of shared files on the same page? It would be easy if it was on a free standing page not a CMS page. Being able to bookmark virtual folders in the shared files was never a goal for the feature.
There is a lot of nuance to this issue and it is not the easiest thing to solve. One possible solution would be to popup a new page for uploading files. In fact I once tried to do this but had trouble getting NeatUpload working from within a modal window. If that could be made to work then the upload could happen in full postback in the popup window and then it could callback to the page and trigger an ajax refresh of the grid to show the new files.