So what format is that repo in? .deb? .rpm? .tar.gz? .ebuild? .apk? There's almost as many package and distribution formats are there are distro's and a lot of them aren't compatible (though yes, the major ones can be converted for the most part).
One of the simplest aspects (the format of the package) isn't even a simple question on Linux. If you want broad public use the distributions need to give up their fiefdoms and standardize on some things the least of which is package managers and library versions (personally I'd prefer RPM go away and DEB be standard but that's my bias). We aren't going to see widespread adoption of Linux until this stuff is sorted out. And that means everyone standardizes and follows each other on things like directories (where things are), packages, libraries, kernel version and certain software (X/Wayland, Audio, init, window manager, etc).
Don't get me wrong, I like the choice (its why I use Linux in the first place), but you aren't going to see someone like Adobe building their software for Linux if they have to target 10 distro's with all different libraries, packages and base software where they can't even predict which glibc will be installed.
I know there is work underway to fix some of these problems (I think wayland will be a game changer, along with systemd and others that have the promise of standardization of key components). But in the meantime you have what Firefox did which is to bundle every library version and piece of underlying software into their package so they ensure they have specific versions they need and that's just not practicable for most software, particularly commercial software. Android is popular because Google did what the community couldn't they created a standard base with a guaranteed foundation to build software on. You are absolutely guaranteed that Android version X on every device has the same libraries and base system and their application store uses version and hardware tables to check comparability and tries very hard to avoid offering software you can't run.
I don't see broad Linux success until the distro's play politics and start compromising and standardizing. Everyone going their own way and doing their own thing only fragments things worse and scares away commercial software. Maybe Google will bring enough of Android into Linux that they basically force standardization but I'm skeptical that the major players would be willing to compromise as they would be giving up some sovereignty in their digital fiefdoms.
Getting back on topic, can Gnome do this? I don't think they can, they're scaring away their own users and shooting for things that don't even appear to be in the scope of the project. But I'll give them props if they succeed, but I'll remain skeptical of their chances.