[Nyororin]

It`s a nice theory - but really is right in the middle of urban legend land.

A pregnancy without a partner is a pregnancy without a partner. You said they go back to Japan to have the babies. No one is going to give a crap about where they got pregnant... No, wait, they`d be even MORE ostracized as they`d gotten pregnant by a foreigner and had pretty much permanently removed themselves from the marriage market (no one will marry someone whose kids are so obviously not theirs).

It`s social suicide, both for the mother and the kids.

If the woman moved outside of Japan and never came back, this would be a totally different story and maybe - just maybe - the differences in ideals would come into play. But that is not what you are saying.

It sounds to me like you`re making up a population subset for your own entertainment. This is not a real phenomenon. I have never heard of a single case of this, short of one poor woman who was raped while on vacation in the US and decided to have the baby anyway... And who moved away in the end due to the sheer pressure of being not only a single mother, but with a clearly foreign child.

In joking, on the other hand, it`s not all that uncommon to say. Women tend to think that half babies are incredibly cute and more appealing than a regular Japanese baby... But would they actually go through with it? No.

ETA;
Thinking about this more - it sounds a lot lot more like culture shock and fear on the part of the mother. That isn`t uncommon at all. It usually happens that the guy wants to live in his country if married, and she is too scared to leave Japan... So the relationship ends and she runs back to Japan. That is a pretty common one. I find it quite doubtful that the women actually got pregnant or gave birth if they did though.