Yes, insurance is effectively a form of voluntary socialism implemented on top of the free market. That's why it sucks so much in the first place. (Which isn't to say a purely market based system would be better; people buy insurance for a reason.)
As I see it, health insurance is uniquely bad for a few additional reasons:
1. People don't treat it as insurance against catastrophic events so much as a subscription for ongoing care, which greatly expands the scope of what costs are socialized.
2. It's often paid for through employers, which reduces consumer choice in deciding what plans to purchase.
3. Demand for healthcare services is relatively inelastic and with modern medicine there's often almost no limit to how much it can cost. If you wreck your car, at most your car insurance company is on the hook for the cost of the vehicle (and perhaps some additional costs up to a fixed limit). But if you're suffering from some disease with no known cure, you could easily spend tens of millions trying hundreds of different procedures trying to find something that will work to mitigate the effects of the disease, and that's an ongoing cost that goes on forever until you're either cured or dead. Somebody has to decide which procedures are worth it or not, and if you're not paying for it yourself that "somebody" isn't going to be you, which creates lots of inefficiencies and is heartbreaking for everyone involved. This is also why we end up with systems such as "in network" and "out of network" providers, and government regulations intended to make things more fair at the cost of even more layers of inefficient bureaucracy.
A few other thoughts:
> If you are anti-socialism, cancel your healthcare and just private pay for your healthcare.
Even for those who might be inclined to do so, this often isn't viable because of #2; they'd be leaving a bunch of free money on the table. I've also heard stories of some healthcare providers charging private individuals many times what they'd charge an insurance company for the same thing, though I'm not sure how common that still is today.
> inserting a group of middlemen into an already expensive system is going to make it more expensive
This is true, though note that government healthcare just replaces one set of middlemen with another.