It really comes down to what an Emergency Room's purpose is. ERs are not meant to be ongoing care providers. They're the "I'm hurt or sick suddenly out of the blue, it's bad and I need to see a doctor asap" place. But they then transition you to somewhere else, who will do the ongoing care.
You break a bone, yes they stabilize you and set the bone. But they don't do the follow up care, make sure it's healing right, remove the cast, etc. That's not their job.
Say you get extremely ill suddenly, like with diabetes. The ER will see you, try to figure out what the problem is and stabilize you. But then it's turned from an emergency to long term management and care. Not their job - by design.
The problem is when people don't have access to medical care on a regular basis, they start to treat the ER differently. Ideally, if you have diabetes, that should have been identified by your PCP, who would have started the treatment so it didn't become an emergency.
But because sometimes things do happen unexpectedly - like some illnesses, or injuries, you need a place for urgent, unexpected care. That's the ER.