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.
If you're 'loading them up on a trailer' to take to an emergency site, you're better off just taking cage-style generators. The stores, nursing homes, and such should already have them. It's one of the reasons I'm against anti-gouging laws. If a store spends the money to have generation systems so it can stay in business even with the power outage, it should be able to raise it's prices to cover the generators*, overtime/hazard pay for employees, etc...
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.
It's about a $3k option. So no, it's not going to be on the cheapest trailers, but it's not 'that' expensive. Especially if U-haul figures out that it saves them money.
Then you get systems like the ford auto-backup. Which IS a vehicle mounted option.
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.
I'm not comparing people traveling to U-Haul. I'm saying that I see the most common trailer case to be that the trailer is rented, the car is owned, because the people are using the trailer for 1-2% of their driving needs, and don't need the trailer around taking up space and still requiring maintenance when they don't need it.
If they're such an edge case like you, that they'd more or less constantly have the trailer on their vehicle, it's time to ditch the trailer and just buy a hybrid in the first place. Do not mistake me for a 'single solution' type of person, though I will get into the 'weeds' when concentrating on a single topic. Once you remove the people who never go that far(I used to drive from ND to NE to visit my parents. Now that the trip would be from AK to FL, I fly), those that do it relaxed enough that supercharger stations would keep up with them(my parents), those that do it constantly enough that they just buy a hybrid in the first place, etc... There's not a lot of trailers left.
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.
I pondered it myself, but kept hitting a wall at the steering issue. Except for backing, a trailer changing steering less than hanging the weight off the vehicle. Plus, I got 600 pounds by looking up the weight of a 22kW generator. Add in fuel, wiring, etc...
So you're looking at needing a way to lift said attachment to place onto the vehicle - which would not be easy, and moving it around without wheels is a pain. I can move my much larger trailer by hand if necessary when it's unloaded, 600 pounds on wheels is relatively easy.
Some early hybrid designs were to feature a removable motor/secondary battery/storage area, but you run into weight/storage issues there - do you want a motor taking up your trunk space when you're going on a long trip?
As for an example trailer consider this article about one in development. 22kW - right on the money! Barely visible out the rear-view mirror, but yes, wider than I expected.
*which, even discounting purchase costs, fuel costs for the electricity to run the store are going to be substantially higher during the outage.