IMHO I would avoid the ublue distros and just go for official fedora spins. The guys have good intentions, but they don’t have the means to maintain that many distros “properly”. I often end up enabling copr packages for bazzite in my fedora install, just to find out the program doesn’t work.
That being said, as the other comments told you, you can still install native apps on immutable distros, it’s just a bit more work. I don’t expect distrobox or toolbox to be much faster than flatpak, as they are all just containers with a nice cli, except flatpak is easier to update. But trying costs nothing