THAT PROBLEM IS CREATED BY THE INSURANCE INDUSTRY
They don't have as much overhead and staff without it.
I work in health care and have seen everything from care to billing, and you are correct about it being because of the insurance industry, but not because of staff overhead (at least on the hospital side). Historically, insurance companies pay a certain percentage on the dollar of hospital costs. Usually around 33 cents but some of the better insurances pay up to 66 cents on the dollar based on the hospital's master charge record, the official cost of their procedures. Therefore, to break even, hospitals have to up their official prices to at least two or three times of what it actually costs just to break even. Of that $325 dollars the OP was charges, the hospital will most likely only see around a $108 of from the insurance company. As for self payers that get charged the $325, hospitals through experience have already written than off as non-payment. Sure some people pay the full amount, others work out a deal after months or years of nonpayment, but that is usually just considered bonus as they never expected to see that money anyway.
Of course, what is happening now, is that clinics are opening up and then contacting the insurance companies and making contracts for a set price per procedure. Thus they advertise their prices which are half to one third of the other hospitals and don't have to have the additional personel or equipment to do things like run tests, diagnose, or deal with inpatients. The regular hospitals are thus having their patients taken away after all the hard work is done. They'd like to redo their master charge record to reflect the actual costs too, but that includes new contracts with all the insurers and getting them to agree to do so, pretty much all at the same time.