Directly run appimages in the sandbox

I was looking into running appimages inside the flatpak sandbox and it seems there is no access to fuse. Is there a way to be able to run appimages directly? I would like to integrate them and use flatpak’s permission management. Unzipping and repackaging doesn’t seem like an option to me.

That’s not possible but there are other options for AppImage:

Is there any technical detail that makes this impossible?