There is no doubt that the Chinese government has increasingly been able to limit the number of FTs teaching illegally in China and to enforce certain qualifications for new Z visas. Multiple posts about this enforcement process confirm this observation.

My question is this: has this significantly limited the number of FTs in China and made it
impossible for schools to acquire an adequate number of teachers?

There's an old native speaker not in the best of health, it seems, teaching at my private school, which is a combined junior and senior middle school. He is approaching 64 and told me he was able to get job offers from a few provinces more easily in the last two years than was possible for him when he was in his mid fifties. Anecdotal evidence, it's true, but it would seem to suggest that the tightening up of the visa regulations has adversely affected foreign teacher recruitment.