Oh yes! Anything but immigration!
But seriously, I feel like this is the broad sentiment of Japanese and the non-Japanese alike. Anti- immigration right applaud Japan for "keeping their country theirs" (as if ethnic Japanese aren't the ones who came later and displaced the local Ainus already living there), and not going on supposed national suicide, unlike the West. Not having enough babies is tantamount to suicide anyway. The narrative then becomes: either allow immigration and go on national and cultural suicide; or don't allow immigration and not have enough babies, which is still considered national suicide. Either way is committing national suicide.
I am not naive to think that immigration has no baggage; but at the same time, if countries want to increase birth rate, then increase the wages and standard of living for young people and families to encourage more people to marry and raise families. However, the elites aren't going to do the former because they don't want to disappoint their shareholders. If they don't want to do that, then allow more immigration, which they also don't want to do.