I would not be surprised to find a better constructed idiot (though I do not expect most people to know) attempting to drive with a trailer.
How to put it? While I'd expect accidents because of the trailer, I'd expect accidents no matter what - after all, most accidents in the country, much less the world, don't involve trailers at all.
Basically, the number of accidents would be at 'acceptable' levels such that U-haul and such would be willing to rent them out. You're always going to have 'better idiots', but that can't be used as an excuse to not deploy a technology unless the results are too catastrophic - and a 'few' accidents here and there are acceptable.
I think it should be something you can disconnect from the vehicle, when you get to your destination, and used as a generator as well as a then-static EV charging platform.
Shouldn't be a problem to provide. A Model S uses 37kwh to go 100 miles. At 60 mph, that would be 22.2 kWh/h or 22.2 kW. Please note that this is a 'napkin back' calculation and is more for estimation. There are many real world considerations, including but not limited to: actual driving speed, any grade, additional drag from the trailer, the range of the EV assuming you're starting with the battery full and are willing to end driving with it near empty, any breaks taken, that you're skipping the 'battery' part which removes a 10% loss step, etc... Honestly, I think 22 kW would be 'oversized' in most situations.
And if a ~22kW generator isn't enough for your camp site...
Adaptive steering is going to help on vehicles that are equipped with it.
It's actually on the trailer. But I'm of the opinion that technological solutions are often superior to education, because education can be ignored, and often ends up being less effective and more expensive(time's expensive).
In the end, consider this: Most of the accidents you've described were to a person's own property. My scale of 'caring': Other people's lives. The operator's life. Other people's property, the operator's property. If they only damage their own stuff, who cares? If the trailers are costing people their lives, the it matters a great deal.
In the end, I think you're picturing a larger trailer than I am. Seriously, what's I'm figuring on would be tiny. How tiny? Not visible from the rear view mirror tiny.
You're also figuring on a 'vast increase'. I'm not, and even if there is, most of it would be on the highway where it's the safest, not on the roads in the cities.
As for added danger - how do you balance this against cars that will do things like apply the brakes themselves to keep you from hitting something? Backing cams?
It may be possible, safer, to simply engineer a method that allows carrying this generator behind the vehicle without it actually being towed.
As you say, such capacity would have to be engineered into the vehicle. You're looking at about 600 pounds for the generator and fuel alone. Well within range for a class 1 hitch that most EVs can take, but they're normally only rated to 70 pounds or so for tongue weight. Hell, it'd exceed the capability for the class 3 on my light truck if you wanted to just suspend it there. I can't put much more than a bike rack or grill on my hitch if it's going to just be suspended there.
Plus, you might not be thinking about this, but it'd affect the balance of the whole car, and not in a good way. So no, it's not a 'trivial matter'.