While the FSF-sponsored repository you suggest might go a (very) small way in ameliorating the problem, it’s going to have next to no impact on the world of real people using real devices. Even something such as you suggest can’t get GPL software into the hands of iPhone users since the only way to do that is via Apple App Store.

However, there’s another issue for app stores, too: by allowing the download of GPL-licensed code, they’re effectively “distributors” under the GPL in the FSF’s view, and obligated to provide source code on demand. Neither the Apple nor the Android store ask, or even allow, developers to upload source code, nor do the stores have any support for providing source code. If source code is demanded, they can’t provide it: they don’t have it. So, simply by virtue of hosting only a binary, they’d seem to be in technical violation of the GPL.

Since they’re commercial enterprises, the various app stores can’t rely on §3(c) of the GPL, either. I’ve gone into this in more detail here