Japan keeps the entire island of Hokkaido running for too few people.[1] The population is dropping rapidly. Most infrastructure is funded nationally, and the rest of the country pays for Hokkaido. Partly because it's only about 12 miles from Russia at the closest point, and Japan doesn't want Russia moving in.
I'm Irish and out of interest I looked up the area of Hokkaido to see how it compares to the island of Ireland and they're actually pretty close - Hokkaido is 83,453KM2 with a population of 5.5M versus Ireland 84,421KM2 with 6.3M. So it is funny to me when you say "Japan keeps the entire island of Hokkaido running for too few people".
Of course, Irelands population is growing while Hokkaido's is dropping...
The rest of Japan also really, really loves Hokkaido. From dairy products to lavender to summer vacation to alpine skiing. Maybe not that many people call Hokkaido home, but tons of Japanese call it paradise.
As for me, I called it the hardest of four islands on which to find a vacant hotel room.
[1] http://www.nippon.com/en/in-depth/a03802/