Yes that's about it. But not just the far right. What the centre left tries to do, generally, is allowing for and promoting (by lots of legislation/rules) lots of bureaucracy.

Bureaucracy can be a real problem with large, public health care. But the same can happen with big insurance companies which can take more risk than smaller ones in investing their funds, creating monopolies that can afford lots of bureaucracy. State monopoly is still preferred to a market monopoly given how each insurance company and health-care provider needs to do the same things as others, having a cumulative growth of bureaucracy.

The thing is, there is a information asymmetry between provider and user/consumer/buyer. Your doctor knows more than you do. That's why competition/markets don't work well.

You could say insurance companies could help you be a better informed user, but they have to effectively do the work of doctors, meaning costs will increase dramatically. Labour costs are (always) high. Health care isn't an exception.

In the US, insurance companies can't only cover generic meds. Effectively, the ability to reduce overall costs has thereby been taken away.

In other words, it's just added bureaucracy. Lots of redundancy.

As there are no real good effects of competition possible, bad effects like advertising and deception are all that's left.

Of course profits can rise because it's nearly impossible to enter the market, since economies of scale are extreme: the more money you have, the more risk you can take and the more you will earn.

You also have little bargaining power, because you don't really choose treatment, you need it.

Only the very worst of capitalism remains.