Not officially but people have managed to reverse engineer it before in order to host their own - https://forum.snapcraft.io/t/lol-an-open-source-snap-server-implementation/27109
Whilst I do get the sentiment (and in no way do I support Canonical in keeping it proprietary), how likely is it that alternative Snap repos are going to show up if they did make it possible? Even with Flatpak where it is encouraged and documented I don't think I've heard of anyone setting up a Flathub alternative of any significance.
And I wasn't aware of the Elementary thing with Flatpak! Admittedly I hadn't really thought of it in that way, I was thinking something more akin to F-droid where there are a couple of extra repos you can add which have applications not on the main one due to slightly looser requirements. But making it specifically for apps for that ecosystem in particular makes a lot of sense.