Single-payer system where one can purchase additional private coverage for cosmetic/unnecessary procedures.
The primary purpose of this would be to remove the negotiation of drug costs from a private insurer who has a profit incentive to a national actor that (on paper) is directly accountable to the public. When a private insurer is negotiating with a private hospital, both parties have an incentive to charge the highest possible price to a consumer as they are focused on covering their costs. That is fine in a service industry such as construction or entertainment ; In the former the end-consumer (be it a casino, energy company, etc.) has the bargaining power and/or capital to adequately supply funds, in the latter the product is elastic, and therefore the "invisible hand" is more applicable. Nobody is dying or going bankrupt because Dead and Company plus whatever venue they're performing at charges an exorbitant premium at the gate.
However, healthcare has such a degree of inelasticity that the B2B transaction cannot take precedent over the B2C. Ergo, a system similar to Japan's Drug Pricing Standard with specific criteria on the innovation and usefulness of a drug is worth exploring. Insurance companies generate revenue by selling policies and/or avoiding payouts, which actually makes their incentives align with promoting health within the insurance pool, eliminating medically unessecarily procedures, and offering low premiums. Private insurers have long been doing what you want done solely by public bureaucrats under the principle of "managed care."
It is the "leading medical professionals, hospital administrators, and seasoned public health officials" you extol that are working to make medical care as expensive as possible with opaque pricing regimes, bureaucratic bloat, and regulations designed to keep doctors' salaries high. Hospital consolidation has given the medical industry monopoly power to dictate the prices insurers and consumers pay.