It seems the problem is not having urgent care at the same location as the ER. Then you triage at the door and route.
The health insurer in this case is actually changing the incentives for the better. Now the hospital risks not getting paid because they didn't triage up front. Unfortunately the patient is caught in the middle here and doesn't have any good option until a less expensive triage option is developed. Hopefully hospitals will respond to insurers denying ER visits to improve their triage as you've suggested.