I was recently asked by a friend of a friend about "Startup culture in Japan", particularly with respect to social entrepreneurship and Fukushima. This is my reply. Take it with a massive fistful of salt, since even though I am ostensibly involved in startups in Japan, there is a stark difference between an American who is peripherally involved versus a native born Japanese person fighting in the trenches day to day in Japan.
"Startup culture" can mean any number of things, from the culture within new companies to the way startups are seen by the public. But From what you mentioned about more "social startup" oriented observations, I'm going to assume that you're interested in what the prevailing attitudes of "starting companies / joining young companies" is like.
As you likely know, Japan is a place where the typical successful career trajectory is to join a large company and stay there until retirement. Compensation plans at these big companies are backloaded, and longevity is rewarded with promotions, social standing, pay, etc. Given this backdrop, staring companies and joining young companies is still very much an unpopular thing to do in a broader context. The most recent new grad employment polls showed that the top 4 places of desirable employment in Japan are the giant import export companies. Students are smart and flock to the best opportunities. They are no different than us in the states, other than those "best opportunities" being different from our economy.
That being said, compared to just 5 years ago, being involved in startups is seen as a much more reasonable endeavor, perhaps because these old big companies are seen as not being as stable and financially rewarding as they once were. Founders seem to be much more visible on media outlets. Funding climate is somewhat improved (though still far behind the States), and some younger people who don't quite fit the mainstream mold as well are finding startups to be a reasonable alternative given the tradeoffs. I see skilled software engineers (who have some of the highest career mobility in Tokyo right now) joining startups that have raised significant rounds and can afford to pay decent salaries.
But whether any of these newer startups (post DeNA / GREE / Cyber Agent etc.) will achieve strong exits is yet to be seen. The latest high profile IPO, GUMI, just hand a spectacular crash as both of its topline and bottomline numbers suffered greatly shortly after its recent IPO. There is a noticeable dearth of large exits outside of mobile gaming. Even LINE (which has an IPO on the horizon) makes most of its revenue from games. Without strong exits, the entire startup ecosystem is on life support. Without exits, funding dries up, wages go down, and talent goes away. Talent is everything in starting a company, and exits trickle down to attracting better human capital.
On the area of more direct "social entrepreneurship", I believe that a company must make a profit and be sustainable as a business no matter how noble its intentions may be. If the company can't make money, then its death is just a matter of time and its beneficiaries (or customers) will suffer in the end when the company inevitably falls. This is in contrast to a nonprofit which could perpetually run in the red operationally and depend on government and foundation grants.
Regarding Fukushima, I think most of the endeavors are in the realm of nonprofits rather than startups. Other than very cheap skilled labor or land in the Sendai area, I don't see very many competitive advantages there. (I do know a guy who went back to Sendai where he's from to start a product design firm there to support the area there).
Regarding daycare centers, there is absolutely a market that is not being served by the currently available private and public options. However, it's a topic that has been in public discourse for at least 5 or 6 years now, so if there hasn't been significant progress by now, I question the economic feasibility of such an endeavor with respect to real estate costs and the customers' ability to pay a price above the cost of operation. Japan's low marriage and fertility rates are legendary now; there are various theories about this, but my thesis (and shared by many others) is that the young in Japan simply do not have much disposable income. That factor would also stifle efforts for childcare startups.
Perhaps there are other opportunities though. For instance, a friend of a friend has started a company that is a "yelp for young mothers", where users rate and leave reviews about restaurants and other establishments that are children-friendly (many places in Japan, particularly Tokyo, are very unfriendly for mothers with strollers, for instance).
If the country feels that this is an important area, then government should consider handing out grants or subsidies or credits, much like what we have seen in renewable energy all over the world (what allowed solar energy to be viable in its early years).