The US accepts a lower percentage of H1b applicants because the number of H1b visas is capped. Other entry routes are less restrictive—most notably via family reunification.
If immigration to Japan were to increase substantially enough, most likely things would change and it would not be so easy even for professionals to get work visas.
And keep in mind that the bulk of US immigration is not of professionals, but of unskilled workers and their families. The fact that the US is able to use immigration to fill population gaps at every economic level is the main reason that it is not facing the same demographic problems that the rest of the developed world is facing.