It’s all the stuff you left out: for example, you’re spending on average 2-3 times more so you’re probably not actually saving more.
Finding providers will require you to spend a lot of time finding doctors, dentists, specialists, etc. who you like, accept your insurance, and are accepting patients. Often the intersection of those things requires substantial travel to areas without transit so how that whatever medical needs you develop don’t preclude driving.
If you did have any real medical needs - even common life events like an uncomplicated natural pregnancy – you’ll need to have tens to hundreds of thousands of dollars saved to avoid needing to negotiate a payment plan. That’s even more pricey if you need medication or care for an ongoing basis.
Because the doctors are for-profit, you’re going to be steered towards unnecessary services and you’ll need to review every bill to make sure only things you approved are listed - hospitals are notorious for having some random out-of-network specialist pop in for 30 seconds to add $15k to your bill.
Because your insurance company is for-profit, be prepared to need to escalate or threaten to sue to have necessary treatment authorized. Your doctor’s medical expertise is secondary to Fred in claims processing, hope whatever you have doesn’t get worse in the meantime!
Also because your doctor and insurance company are for-profit, expect either of them to stop doing business with the other any time it’s more profitable. There’s no guarantee that anyone in-network will be available in your area and you’ll likely need to haggle to get permission to go out of network.
None of that is great to deal with while your family is caring for someone with whatever issues need testing and it’s made even more fun by the knowledge that almost nobody in what you’d consider a peer country has to deal with anything like that much hassle.