"Have left" is used here to indicate that as a result of or due to the plummeting birth rates, there are many Japanese couples without children. While this reasoning does seem a bit circular (obviously couples choosing not to have children is what causes low birth rates, not vice-versa), based on the context, it appears that the article is trying to describe the overarching trend of not having children -- represented by the plummeting birth rates -- as resulting in many couples lacking children and needing to fill that void with a baby robot. Of course, more context would be necessary to say this for sure, but that's what I get from the sentence provided.