I don’t mean to sound snarky here, but: if you believe you can boil down one of the most fractured, complex, and heavily regulated industries (really, set of inter-related industries) in the country to a single “that group of assholes over there cause all the problems” bulletpoint, you have missed 99% of the story.
There would be incidental costs, like more unemployment, and possibly some more admin within the healthcare system; though from what I hear it would more probably reduce admin costs on the healthcare end too.
Well, that's partially because they're legally required to spend 80% of premiums on patient care.
The end result is that higher premiums mean higher profits out of that fixed percentage of margin they're permitted to skim, so they don't fight cost increases too much - until people outright stop being able to afford the premiums, increases in them benefit the insurer's bottom line.
People see a lot of money flowing into insurers and hear about large profit numbers. That makes it feel like they're the obvious problem.
Ending that scam and asking patients to add an extra percent or two on their bills to pay for good food and a good environment would barely be a rounding error compared to the banditry that forces them to pay outrageous and unjustifiable fees for common meds and routine medical services - never mind specialised care.