The problem is that insurance companies would refuse to insure people with pre-existing conditions . . . not just decline to cover the pre-existing issue but decline to insure them at all.
It's more complicated than that . . . but that's the quick and dirty version.
Basically, if a person has health issues and for whatever reason they have to change insurance (new job, lost job, can't afford old insurance, etc.) prior to the ACA insurance companies could and would refuse to insure them. Canttakeitanymore is spot on with his point about risk pooling. This is one of those areas in medicine where there is a somewhat awkward intersection between necessary care, profit margins, and morality. Touchy subject with high emotions.
I don't necessarily disagree with your point but I think it would get pretty hard to decide what procedures were only due to the pre-existing condition and which were new conditions. For example, if you had back surgery then developed a staph infection from the incision, was the infection an extension of the the back problem or is it a new issue? If you had stomach cancer then later developed liver cancer, how would that be handled? Some things would be obvious but a lot of others would just lead to more legal battles, costing more.
Also, a certain company might not insure them but (and I'm no expert at this so someone can correct me if I'm wrong) aren't there high-risk pools that people can get into? I believe this was reference earlier. So it's maybe not so much that they can't get any insurance, just that they have to pay more for it.