Everyone who's saying that the low birthrate is a good thing because Japan is overpopulated doesn't understand what the exact problem is.
As was mentioned in the article, Japan may have a lot of people but the low birthrate means that the population is getting older. This is a problem for them because when they become so old that they can't work anymore and need to retire, essentially becoming unproductive resource hogs, there won't be enough young people around to support all of them. (And, naturally, professors like the one in the article tend to be getting up there in age themselves, so this would probably be something that concerns them.)
Something similar is happening in Germany, and possibly in other places as well but I haven't heard about it yet.
This silly solution probably won't work since it's more likely that the young people in question have made a decision to not have children, rather than just being socially awkward shut-ins. The only solutions I can think of that wouldn't contribute to overcrowding are encouraging adoption from other countries, somehow outsourcing foreigners to do Japanese jobs, or...euthanasia. Which would be a difficult option for people to embrace, for obvious reasons.