Very few developers actually attempt to do this, on any platform— virtually none, as far as I can tell. It's slightly more common on macOS for developers to actually try to emulate or reuse the design language and look-and-feel of the base system. But on every platform, it's extremely common for GUI apps to just throw the design language and other details of platforms they run on completely out the window. It's the M.O. for the most popular cross-platform toolkit right now (Electron). For every app that maintains multiple UIs, there are at least ten that do that, maybe a hundred!
Besides, COSMIC doesn't use a new graphical toolkit. It uses GTK+, just like GNOME.
But even without them caring for UI/UX, the proliferation of DEs, even with common UI toolkits in the Linux world means they spend a lot of time and energy working on bugs that are not true bugs but are artifacts of a UI theme that the developer did not consider while developing their app.
For example, it's almost certain that the unified tooltip in COSMIC will lead to bugs complaining about how users are unable to drag the window by clicking on the chrome. In this case it would be fairly easy for a dev to close the bug because this is such a prominent and obvious difference in COSMIC. But there will certainly be other UI differences that will not be as easy to pin down to being the result of COSMIC's UI changes, and will not be as easy for devs to close.
Ideally, that's what the freedesktop.org specifications help with. You build against the specs and interfaces, and the code should work across DEs that implement specs from freedesktop.org. In my (albeit limited) experience of writing against freedesktop.org specs, it works pretty well.
Heck, many apps are web-based and uses electron anyways, and those are generally multiplatform anyways.
I think if whatever app they make/port worrks via Flatpak, it should work on all/most modern distro.
Edit: it's GTK so no problem
System76 is only adding to that mess.
And that's the problem with the proliferation of DEs. Applications, which range from having no developers actively working on them, to the best teams at Microsoft working on them, have to handle yet another DE, and have to deal with the bugs raised by the users of yet another DE, etc.
UI/UX is hard enough to begin with, but requiring devs to either maintain several UI/UXs, or try and come up with a design that works across the proliferation of DEs is highly counterproductive.