I don't have the numbers, but anecdotally from looking for an apartment with my SO, there doesn't seem to be a big housing availability problem in Japan. Available apartments are plentiful, and outside of central Tokyo, Osaka etc, are priced reasonably. It's a far cry from the situation where I'm from in Sweden, where you have to be on a waiting list for 3 years to get your turn at a rental contract since there are just no apartments to be had.
Young people in Japan live with their parents due to lack of jobs. The Japanese employment market has recently had a massive shift towards part time labour instead of full time labor, leaving young people with jobs that can't support them.
Also, Japan has had a solution for the "opportunities for sex" issue for decades - the massive amount of hourly Love Hotels that are scattered all around the country (and people aren't shy to use - I've had to queue for one).