It's not an access problem, it's not an insurance problem, and it's not a quality problem. The quality of health care here is the best in the world for those who can afford it.
There are several things that push the cost upwards. Salaries, hospitals that look like spas, litigations, the insistence of having the very best regardless of the cost, the fact that so few people feel any pain associated with an expensive procedure or unnecessary ER visit, the relative absence of free market forces.
Unfortunately the current administration, I believe with good intentions, misdirected their efforts on insurance instead of cost. As a result, costs have actually gone up. But the OP linked above is correct, the cost is out of control. (Btw, I am in the health care system, and am therefore likely part of the problem.)