I'd argue that US parents are so keen on schools staying open because often their jobs depend on it. I expect it would be similar in Japan as well.

Maybe it seems like daycare because, in a sense, it does serve the function of allowing parents to work. That doesn't mean it's an alternative to daycare. The parents want their kids to have an education, but they also count on school to be able to work.

Even here in Canada, if a school has a snow day and an employer doesn't, it can be a little tense if you don't have anywhere to put your kids. People with relaxed employers and good leave options are fine, but many people don't have that.