Some method of notifying users of an updated plugin would be great. I'd be concerned about automatic updating as a general rule - some plugins may change names and need the old one uninstalled, and certainly as you mentioned the Calibre version has to be checked.
Each plugin could check its own status - but that's adding a lot of extra code to every plugin.
As a start, just a plugin that scraped the info from the index and presented the list of plugins available, highlighting the ones installed and if there are newer versions available (and a link to where to get the version) would be a big start.
Actually, most of that is there by just going to the Index page
I'd guess the format of the information on the Index page would need to change/standardize to make it easy to extract, although what's easy to read for a plugin isn't always as readable for users.