I have a similar problem in Europe too. Most of the good public state-insurance doctors are overbooked and my option is to keep calling every doctor on a 50km radius continuously, hoping to find a free specialist with an appointment, or pay up privately out of my already small paycheck for a spot at a private doctor.
>hotels losing your reservation, airlines overbooking flights, mail and deliveries disappearing, people promising and not returning calls, etc.
That doesn't sound like anything US specific but more like a collection of things from the "shit happens" category. Same things can happen in Europe too, and some have happened to me.
I think you imagine the grass must be always greener elsewhere. It's not. Every place has its own set of perks and problems.
The databases that maintain this information are not always accurate or up-to-date. So the doctor might say one thing, the insurance company another, and both be wrong in subtle ways. Nobody knows what's going on. It's often a crapshoot what you'll owe after a simple doctor's visit, even if you've asked all the right questions and stick with the same doctors.
More examples: budgeting flexible spending accounts, choosing health insurance annually, finding doctors in your network (and checking again and again, with multiple sources), hotels losing your reservation, airlines overbooking flights, mail and deliveries disappearing, people promising and not returning calls, etc.