I was towed once on a flatbed about 150 miles. That was after the unfortunate transmission explosion years ago.
More recently when I was sorting out my combo-problems of the Crane ignition and bad power to the fuel pump, (both issues long since solved) I had to be towed about 15 miles. Called for a flatbed, but a regular tow truck shows up. The guy told me, "we didn't have any flatbeds available", and then said, "don't worry, I do this all the time on [insert name of classic/vintage car here] and never a problem."
The big problem was when he went to put the magnetic brake lights on the trunk deck. "sorry, I don't want you scratching my paint, but more importantly, it's aluminum". "Not a problem, I'll just place them on the doors"
I convinced him to just go slow, forget the darn lights, and take local roads. Sure enough, we made it without an issue.
But I lost som hair that day--best to have a flatbed...more importantly, best to have a reliable car!