Its also no different than patina in that it has nothing to do with traditional hot rods, and is a modern aberration. But then, lots of guys on here dont give a rats eek *** about traditional hot rods, so there you go...And I like the pleated top insert s**** metal posted. That actually DOES have something to do with traditional hot rods.
Lots is times it seems to go hand in hand with hidden hinges, suicide doors, flush fit doors. Things you see done on a lot of those overly smoothed out street rods. Posted using a number two pencil on a paper napkin.
Check out Rusty model A thread he filled the top flush mounted the doors and it's the furthest thing from a street rod. I agree with most of the other posters that leaving the top off looks more rat rod than traditional. It may not be a model a but my cars top was welded in and the door handles were shaved in 1959.