Anybody who goes abroad, even in the EU, without decent insurance is an idiot. Much stuff is not covered by EHIC. the biggies are air ambulance home if you are not in a condition to take a normal flight, and repatriating a deceased body home. I had a family member die in Rome - no insurance. The cost of bringing the body home was massive. We did a funeral in Rome (getting an atheist funeral in Rome is almost impossible, but we did it) and even getting the ashes back to the UK cost an arm and a leg.
Then you have to translate the death cert for closing down stuff....
Even if you fall ill in the UK, and you are away from home. Imagine being hospitalised 4 hours drive from home. What does your family do? Stay in the area - but that can cost a lot. or go home and leave the ill person on their own. I dont think the NHS will arrange an ambulance from Truro to Carlisle!.
To counter that, your health insurance may be invalid if you have a fall after a couple of strong beers, or if you do crazy stunts on water bikes etc whereas the local A+E will glue you back together again under the EHIC. So it's swings and roundabouts, after Brexit don't get paralitic (a good thing IMO) and check thoroughly you are covered for climbing up things, swimming under things, jumping on things and getting hit by your own golf ball rebounding off your mate.
Your final point, I think if absolutely necessary an ambulance would take a patient from one end to the other and with a chaperone too, although an air ambulance might be more appropriate for 800 miles. If it isn't then it's a question of where do you draw the line, 10 miles, 30, 100??
If, for example, my old lady was taken ill in, say, Windermere, at some point after discharge she would have to get home to Bolton - and if a taxi/wheelchair car was out of the question then I assume they would provide an ambulance on discharge. She wa s moved 10 miles last year to home when car/taxi was inappropriate - so where's the line?