This scenario seems contrived to me. You'd have to have an emergency immediately upon the termination of a trip during which you'd completely exhausted your battery.

You can run out of gas in an ICE car too, and then it's even worse because you need to go track down a gas can instead of plugging in. The simple solution, of course, is to never fly that close to the Sun.

With a gasoline car, you can in most cases drive to the next gas station, and get enough fuel to get to the hospital within 1-2m. With an EV, you have to wait. Did I overlook something?

The scenario of an empty EV battery is not that unlikely. Eg you forgot to charge when you returned.

In an emergency, you surely call an ambulance, not drive yourself.

Not really. Where I am that'd take at least double the time. Depends on what kind of emergency it is, of course, I'd not move someone with spinal injury, but if my girlfriend is feeling terribly sick, I'd rather drive her (that's an actual real life example that happened to me).

Depending on your insurance, ambulance and emergency charges can be either rather high copay or only % covered, and are NEVER cheap on their face.

My wife drove me to the emergency room on a 3am Sunday morning when I felt like someone was pushing a golf ball out through my ribs and I had my gall bladder out that week. $750 copay for ambulance service.

I am aware that the ambulance is not free in the US, but it's quite hard to comprehend I guess. Especially in an emergency, I wouldn't think of anything other than calling one, driving to hospital myself wouldn't even cross my mind.

Yes, but you're talking about a maybe once in a lifetime event here (need to rush to the hospital, but you just got home with your EV on 1% battery). Just eat the ambulance bill and curse your bad luck.