The only problem it solves is burned out employees, and I would argue that it doesn't even fix that problem. The reason is that you can't force people to take their minds off work, even if you force them to not physically be at work.
This seems like a non problem to me.
Everybody hated that too. Being forced to take time off when you didn't particularly want to, and not being able to "save up" enough vacation for a really good ling trip away...
And, of course, those rules were regularly "bent" when it suited management, but rigidly enforced otherwise...
(We typically accrue 20 days per year here in .au, so that pretty much means after 18 months, if you haven't taken any vacation at all yet, you need to take at least a week off in the next three months, and a week off every three months thereafter.)
As Japanese workers are famous for not using all their paid leave, and if they do it is in half days here, this is a nationally mandated way to make sure that everyone gets at least a few days off a year.