I will try to go in order.
I would anticipate a large increase - especially at certain times of the year like traditional holidays and traditionally travel holidays, where the number would be quite large. I also expect the overall number to be much larger than it currently is simply because people are going much further than the ~250 mile limitation.
As for using it as an external generator? I think that would make an excellent scenario and would be an added bonus. Even greater would be the use of that to help keep humans alive when disasters take out the power grid for an extended period of time. Load up a bunch on a truck and then use smaller vehicles to transport them out to the various sites. If they were built at different sizes, perhaps for a size for an EV freight-hauling vehicle, then those would likely be larger generators and maybe could handle powering a small store, a nursing home, etc... That might be a good bonus.
Ah - I was thinking of the adaptive steering that I can get (and did order this time but have not used it as it was not an option on the test-drive vehicle) on my BMWs. Those allow, at speeds less than 30 mph, the rear tires to turn in conjunction with the front's turning. I did not think of putting them on the trailer and that does seem like it could mostly resolve most every "in reverse" situation that I can think of assuming a computer controls it. I expect it to be expensive (even if artificially and no I do not suspect the market to correct it with any great speed) and something that is not included on lower-end models.
As a trivial aside, I did consider the hybrid i8 (a beautiful car - you should check it out, hell, I dug out a link for you: http://www.bmwusa.com/bmw/bmwi... -- that may be fun to spend a minute or two looking at) but I just could not justify it as it did not suit the needs I had set for myself. It is a hybrid currently but there are plans to turn it into an all-EV as I understand.
Again, yes, I think it will be a vast increase. Many cars on the highway are from out of the state. These people are traveling for a variety of reasons and I do not think that they will want to stop that practice. I do not think they are going to want to wait every few hours to recharge.
Also, these are people traveling. They are not just people moving. Comparing them to a rental such as U-Haul is intellectually deceiving if not intellectually dishonest. With a 200 mile range I could, barely, make it to the nearest real town (one with actual hotels that are not just tourist traps, stores beyond a small grocery store or the *singular* general store, and other amenities like a movie theater. This is actually a common drive for many in my situation. I am using the various reports I have read and reviews as it is more like a 160 mile trip (both directions and yes, if I could find some spot and stayed in that one spot while in town I could charge the vehicle).
My trip requires things like heat and sometimes actually should include AC. There are many very large mountains that I must trek over as I work my way down into the foothills of Western Maine. To go any further than that, again a fairly common thing, would need extra capacity that is not yet available. The up-thread stated 200 mile range is not adequate. Make it 400 to 500 (800 would be wonderful) and I will be in line to buy three. One utility, one sedan, and one sport.
You are correct, I was picturing a low-slung and wide trailer. I figured the lower center of gravity and the lower profile would be good. The first for the stability and the second for decreased wind-resistance. I was not picturing someone traipsing around with a covered stand-up Honda generator but that could work. Again, a wider and larger trailer would be ideal for control but the adaptive steering you mention could be the solution. It should not even require a lot of work (or space) beyond the computer and steering mechanisms. One might wonder if we want the extra complexity as it creates yet another point of failure. That can be maintained and can be worked around - it has potential. It should be interesting in the snow, especially when the car goes sideways. Even more interesting will be when the driver is unfamiliar with driving in snowy conditions or has not done so in a while.
Finally, I think I got them all up to here, I did think about the weight but I did not give it much thought. We have adaptive, custom, and pre-configured adjustable suspensions. It may (most likely will) require that the strut and coil assembly be rated for a higher weight but that can be dampened programmatically. This will, no matter what we do, impact the handling profile. Some suspension changes can mitigate this but I doubt it can be negated easily or efficiently. My thinking is that the typical "universal" receiver hitch assembly could be configured to tie into the vehicle deeper, have more attachment points, and use a bit more bracing if needed. I am thinking something akin to the Reese hitches.
The class 1 hitches should have a 200 pound rating for tongue weight. 600 pounds would put one at a class 4. I would also hazard a guess that, in the end, these would have varied capacities and varied weights. There are some pretty decent and efficient generators out there (a vast improvement since I was young in price, capacity, and quality) that do not weigh a whole lot. Fuel is along the order of 8 pounds per gallon so we'd need to factor that in. 600 pounds may be a bit high but would likely cover most eventualities and it seems that it could be done directly from a receiver hitch. An alternative is to simply set a standard and mandate it be built into vehicles.
This does not discount the idea of a trailer, it is simply another line of thinking that I have been mulling over since first pondering the trailer idea.