I've seen this type of functionality requested/mentioned previously on here going back quite a while. I'd like to be able to refresh a module when clicking the "New updates from the feed" button (and even the scroll to load more). I haven't looked at the javascript/ajax that is powering it but seems feasible in theory to have a hook that a module could associate with. A few examples of how this would be useful:
1) Banner ads. If you have ads on your site and your users are parked on the primary community page you are getting exponentially less ad impressions because the ads do not refresh on user actions as they would on a page load. In short, you are earning way less revenue than you should be earning. Some webmasters combat this with auto refreshing ads, however this is against google policies for example, so you'd run the risk of getting blacklisted by Google / Adsense if you use the auto refresh of a page or even just the module (this can be done).
2) Social features such as Online Users. You might have users that have your social site online for hours a day yet the online users module is only accurate from the first page load. Some users even leave a page open for days at a time so "birthdays" for example may be severely outdated.
3) If you have other active features on the site that are regularly updated you might have modules in place to display the latest (e.g. latest news, newsflash, blogs etc) But without refreshing, the user attention to them is negated other than if they are in a stream item. Even that is negated fairly quickly if you have an active site with a fast moving stream. If you have timely or competitive content this is a killer for your site not to have your content fresh to the users' eyes.