I ssuspect we might almost be better off. Just because we would not have the NHS doesn't mean having a system like the USA.
Many countries have far more efficient systems that are essentially state funded. All most all EU countries do. In France it is a mix of state funding and mandatory insurance. Those on lower incomes do not pay for the insurance. I am sure there is a GN member who lives in France, who could fill the details in.
In 30 years of having a house in France we have used the French system twice. Once when DH went down with a severe respiratory infection. We took him to A&E, he was quickly triaged and taken to a waiting room with comfortable adjustable arm chairs for those who were clearly unwell, with blankets and pillows. Once seen and exrayed he was given a prescription, which we had to pay for, about 12 euros and a few months later we received a bill for treatment - 30 euros.
Similarly, when our DGD, then a year old have an allergic reaction to touching a tomato, we rushed her down to A&E, were immediately sent up to a paediatric ward where she was seen immediately. They kept her on the ward for some hours until the swelling and rash began to clear. later we received a bill for 8 euros.
To assume if not NHS then USA when there are so many other countries with better health care and effectively free health care is just perverse. Many of them have far better outcomes than the NHS.