If you could press a button and get shot of all the private Chinese English schools in one stroke, the knock on effects could well mean you'd be deleting your own job in a Chinese state school.

The strange thing is that many ads for FTs for the private sector do not insist on job applicants meeting the minimum requirements academic qualification-wise that have been stipulated by the Chinese authorities as necessary for the award of an FEC and hence a Z visa. Surely this means that there will be FTs employed by private English schools in China who would be ineligble for the vast majority of public schools/universities that almost always demand their FTs to have a university degree. The so-called unqualified FTs employed in the private sector at present are almost always marginalized re getting alternative employment in the public sector.
It's true that GWs in the private sector with degrees and TEFL would switch to competing for public sector jobs, but not by any means many of them - they would dislike working for average pay in small cities and counties where it would be difficult for them to find second jobs that would occupy a large proportion of their free time to enrich themselves to some extent by working the kind of long and unsociable hours overall they formerly put in at private schools. Since they are qualified academically to get working visas in other countries too, I suspect they'd apply for private sector teaching jobs elsewhere instead of continuing their teaching careers China.
As I prefer teaching in the backwater places of China that have neither Western fast food chain restaurants nor more than a couple of Westerners in town, I doubt there would be increased competition from ex training centre GWs for the kind of public sector jobs that I choose to apply for.
The reason I am against the private sector of EFL teaching in China is that there are too many horror stories emanating from there about FTs being used and abused! I shall discard the kind of self-serving reasons you suggest for keeping Chinese private English schools open. They should all be closed down for good by the relevant authorities here, and the sooner the better, that's my view!