I think app stores are a popular concept today not because they are original or innovative, at least in my opinion, but because they are simple for the user to understand and (ab)use. After all, an app store is nothing more than a remote repository with search indexes and download facilities...uhm...sounds to me like a software repo we already have for linux and unix (and mac os). What is interesting about an app store is the visibility it gives to your application.
Besides this, I don't think we will never ever have a single way of app store when dealing with different operating systems. We cannot even agree on a format for current projects (ports, deb, rpm, pkg, ips, opencsw, tarballs, exe, zip, dmg, ....) and being Qt a cross platform developing environment I don't think we will have easily one for it.
Even getting a cross-buildfarm will not be so simple due to different dependencies (databases for instance). Maybe something can be achieved with plugins, but it sounds to me that each big vendor will have its own distribution store.
By the way, the app cafe used in pcbsd is a qt application that works as an app store. Quite simple, easy to work with, and worth to mention not because works for qt, but because is built on top of it.