That isn't what "directly subsidized" means, though, that's "directly run". A subsidy is a strictly monetary arrangement, not one where the government actually becomes the employer.

Tricare is perhaps the closest thing we have to direct government healthcare, it handles healthcare for active duty military, it is part of the DoD and contracts out to providers directly (including therapists) and compared to other private insurers they are among the most difficult to work with. My partner is an independent psychotherapist and contracts with various healthcare providers and Tricare has by far the highest rate of spurious rejections, short paychecks, heavy audit requirements, etc and their resolution department is the hardest to work with.

So we already have evidence of how it goes when the government manages it directly and it’s worse than private industry.