That would break the system completely. The only reason any of this holds together at all is medical providers shift costs from one patient to another. Medicare doesn't pay enough for the care patients are provided, so hospitals charge private patients extra. If you introduced price caps either hospitals would start to go out of business or they'd stop accepting Medicare entirely.

Price caps always and everywhere cause shortages, including long queues for certain types of care. This may be acceptable but we need to understand the trade-offs when making any changes.