Earlier quoted context omitted.
This is a good idea. Why carry round all that weight 100% of the time when you can only take it when you need it.
One of the issues with that idea is you need very heavy duty connectors, EVs are hundreds of amps coming out.
It can supply energy slowly, perhaps at dozens-of-amps.
The only time when an EV gets into hundreds of amps territory is when it is doing real work: Work like accelerating, or going uphill (or both).
Maintaining a speed on a straight stretch of highway is not a huge burden in terms of work, and that is where I think that a trailer-mounted battery might shine brightest.
The car's internal battery can take the brunt of rapid acceleration tasks and get filled back up over time, just like it already does in normal charge-daily EV use.
So to put some of this into real terms:
20A at 355V is 7,100 Watts, or about 9.5 horsepower. That's a ton of real work.
100A at 355V is 35,500 Watts, or about 47 horsepower. Way more than plenty to keep a portly EV heading down the highway.
The connection for the trailer APU doesn't need to handle the peak current draw of hundreds of amps. It just needs to be able to (slowly) pick up some slack and thus provide greater range.
Like the BMW i3 with the gas-fired range extender: The EV drivetrain could consume a ton more peak power than the built-in genset could produce, and that's OK.
It's not like people are using these in endurance racing or something. Most real-world driving is pretty mundane, with only occasional instances of rapid acceleration.