Since the question was "Ctrl-z works universally", I feel obliged to point out that ctrl-z sends SIGTSTP, which can be blocked--not to be confused with SIGSTOP, which cannot be blocked. I don't know of any program that does intercept SIGTSTP (except a test program I wrote that tries to print the name of any signal it receives), and I suspect that "polite" interception would be to release a few resources and then accept being paused--but, in theory, a program could ignore it.

Many curses programs (for example vim) intercept ^Z to set the terminal back into a more normal mode and then pause.

This is probably a stupid question, didn't know about bg and fg before. But after playing around with it, it feels pretty amazing, why even use screen/tmux when you have these?

Screen has aaugh easier interface for multitasking, including things like stderr not bleeding out from whatever background tasks you're running. Not to mention that switching back and forth between screens is what it's designed for and thus a lot easier than switching between job numbers. Also the ability to detach your screen and its running processes from being coupled to a specific login session, which is probably the main reason I started using screen instead of multiple terminals in the first place.

With bg, it is likely to suspend itself again by attempting to read from the terminal (which a text editor is likely to do basically all the time).