Yes, there are real planes sometimes used in movie stunts for doing crashes, it's not all CGI, although most is, doing real things like that costs a lot of money.
But regardless, if "not scaring fly-scared people" was actually a concern, any planes crashing in movies would be forbidden, not just real planes crashing in movies. But it's not.
Not likely given the broad sweep of the First Amendment. Much easier for the FAA to deny a license to crash a plane under various safety rationales than to say "you can't show that because of the message" in the United States. The latter is almost certainly unconstitutional.
