What I've seen here is they don't mind rusty (seriously bad structure) classic cars driven around.
The biennial 車検 ('Sha-Ken', from Jido
sha Kensa Torokuseido - the Japanese equivalent of our MOT test, but a lot stricter) would normally be expected to detect such cars and fail them.
I see you're in Japan with Dave W of the self-styled 'GTR Heritage Centre'. Dave knows a good bit about finding rusty cars in Japan. Here's one he sourced, imported and sold in the UK after describing it as "immaculate":
But generally speaking, I'd say the situation in Japan is not all that different to here in Europe and UK. Plenty of early 70s cars went through a dip in value in the 80s and were subject to make-do-and-mend type repairs. Values started climbing back up slowly and some of these cars survived in better condition than others. We are often left to deal with the legacy.
But just like here, there are plenty of excellent old cars in Japan and there are many small businesses involved in amazingly detailed and accurate stock restorations. They tend to be artisan types who are introduced and recommended through word of mouth. It seems a little unfair to focus on the occasional sh*tboxes that might be floating around semi-legally.