There are many reasons why you don't want to do this. Flatpaks dont touch PATH, the sandboxing makes it difficult, and flathub doesn't distribute CLI programs, being the main ones. So yes, it is technically possible, but so cumbersome as to be unfeasible. Snap on the other hand does implement a pretty frictionless method for running CLI snaps.

Again, you guys are making me defend snap, I'm not even an Ubuntu user. However, when you blindly state things that are incorrect, you denigrate your own position. This whole snaps are slavery echo chamber is extremely tedious. Its no different than people just parroting political opinions they saw on instagram. Use the best tool for the job. If that's Ubuntu, great.