What is broken about it really? Having been insured my whole life, I've never dealt with hospital issues, and we've had several major medical events (complicated pregnancies mainly, lots of time in the emergency room, etc). For the most part, I pay the max out-of-pocket every year, and then I pay nothing more. It's not particularly difficult to deal with.
The only annoying part is after your first ER / doctor visits each year, you end up with a bunch of different random charges from people that you have to pay separately. It's an annoyance, but hardly one that requires us to 'burn it all down'.
This year I have an HDHP and an HSA, so I have more of those, but I also have an HSA.
As an example, my wife's first pregnancy probably cost about $200k nominally, but I paid... $2000-3000 at most.
The only real 'issue' I see is the tying of health insurance to employment, but there are straightforwards ways to get around that (federal incentives to purchase your own health insurance, and then employers can pass along savings so employees can purchase themselves). For me, I've never been unemployed longer than COBRA so it's not been an issue.
There are a lot of good things about America's system. My wife's pregnancies are extremely complicated. Many doctors said to give up. However, we searched and searched for a doctor to help, and we figured out what works. Basically, for unknown reasons (although many plausible ones that cannot be confirmed), she needs to take an expensive blood thinner during pregnancy or the baby dies. Since her tests don't come back for the 'standard' conditions this works for, it is difficult finding a doctor willing to prescribe. In fact, we didn't even know it was an option, until we went all over the country to various experts. Due to the free market, we were able to get to these experts in a matter of weeks. Similar experts in countries with socialized systems have long queues.
When it comes to the medication, due to the fact that we are the ones that pay (via insurance), not the government, as long as we can pay, we can continue to live our lives and have our children. Based on our conversations with other women in my wife's position in countires with socialized medicine, they have to really advocate for themselves in ways we do not in order to get their government to even provide the medication or pay for it. Many wait months before they are able to get someone. Every once in a while the government revokes access because some bureaucrat says it's not medically indicated. We've never had that. Should her doctor decide to do that and sentence our child to certain death, we have several backup doctors willing to prescribe the medication. Some moms in other countries we're in contact with have been cut off from the medication and subsequently had miscarriages in the second or third trimester. This is insane. I'm glad to live here.
We recently moved, and just scheduled a bunch of appointments and asked the doctors point blank whether they'd consider it based on her history. Some said no, others said yes. In a few weeks, we figured out what her friend over in Canada took many, many months to figure out. When it comes to pregnancy, months matter. 24 months of waiting can drastically change the spectra of outcomes in a women's pregnancy, especially given the age at which many women have children these days.
Same with things like surgeries and such. My relatives in countries with socialized care are waiting many months for things Americans get in a few days.