The American health insurance system is not insurance--it's a long-term payment plan. Why does insurance need to get billed when I go for a yearly checkup with

The American health insurance system is not insurance--it's a long-term payment plan. Why does insurance need to get billed when I go for a yearly checkup with my doc, or when I pick up some prescription-strength ibuprofen? My auto insurance company doesn't get billed when I get the oil changed in my truck. My homeowners insurance company doesn't get billed when I have to recharge the refrigerant in my heat pump. The insurance companies have taken all the monetary interactions between clinics and patients away, except for the (oftentimes criminal) balance billing that occurs when your claim was denied for some ass-hat reason like "You didn't tell your insurance company whether or not you had other insurance."