"What we should do is refuse entry to anyone entering without insurance..."
I've visited Cuba a number of times. On arrival a number of visitors (around one in five or so) are randomly asked for their travel insurance documents. Those who cannot produce proof of cover are charged a flat rate for their stay (I believe it's something in the order of £25 per day). It's done as they take your photograph (which is examined when you leave to ensure the person who arrived is the person leaving), examine your entry visa and your passport before you set foot "landside" at the airport. It's all very simple and just requires willpower. You either produce proof of cover, pay the flat rate or are denied entry. It's made well known to visitors:
https://www.gov.uk/foreign-travel-advice/cuba
Can you imagine a foreign visitor pitching up to a BUPA hospital declaring "I need some kidney dialysis whilst I'm here so if you'd kindly sort it out for me - free of charge of course". Why should an NHS hospital be any different? The NHS needs to get real. About £1 of every £7 collected in taxes is spent on the NHS. The immigration authorities have a responsibility to ensure those arriving will not lay costs on that budget and the hospitals (with their armies of scribes and administrators) have as well. Taxpayers are e simply being taken for a ride.