The idea that once you have insurance the problems just magically go away is wishful thinking. These companies are predatory and stupid, and if I hadn't taken the time to read every single line for the 4-page, 10-pt font bill they sent me I wouldn't have even known they were charging me as though I was uninsured.
In the age of high deductible plans I'm not sure this is accurate. For many Americans the $5,000+ for a deductible each year is unsustainable, especially if someone on the plan has an ongoing issue or they have to meet the deductible multiple times (changing jobs or an issue than spans calendar years).
Without the ACA, this wasn't possible for millions of people. With the ACA it was still too expensive for millions of people. With the ACA minus the individual mandate it will be too expensive for even more.
Also before the ACA, health care plans came with yearly and lifetime coverage limits. Coverage limits that were far below what care would cost in many cases. So even with insurance you could still face financial ruin.