A rent cap is a clear sign that the capitalist system is broken and we need a better system to match the housing needs and supply without feeding into heartless vampires who'd rather have empty apartments than rent them at a reasonable price.
The capitalists instead decided to optimize for steadily increasing the price of housing by restricting supply, so these are now primarily seen as an investment with nearly-guaranteed returns, rather than places for people to live.
Or "magic coin-shitting machines", as Charlie Brooker so pithily put it.
Either way I would say housing in Japan (considering all the constraints) seems to work great.
No. Very little. Just read articles over the years saying they are facing similar issues of real-estate bubble and speculation and that prices in Seoul are getting close to those of New York.