[nradov]

Which specific regulations could we remove to cut prices without seriously impacting care quality?

Generally the level of regulatory compliance necessary to enter the healthcare market is proportional to the risk of patient harm. If you want to sell healthcare analytics software not directly involved in patient care then there are basically no more regulations on vendors than in any other software market. On the other hand, if you want to start a new company to make implanted pacemakers then you'll have to spend years working through FDA compliance issues because a single tiny error can easily kill a patient.