I can't imagine any benefit to aggressive treads on a trailer tire.
We camp mostly in the deserts where we ride, so we tow a lot off-road. We camp in pretty large groups and I've never seen anybody with off-road tires on their trailers.
You need good traction on your tow vehicle tires, but as far as the trailer goes, I think the only criteria are:
* Follow me in a straight line
* Hold air
* Don't pop and shred my fenders
* Look black and pretty and don't detract from my beautiful trailer
We pick up a lot of nails & sticks out there, so I've plugged a ton of tires. I don't keep a log, but I'd say I've plugged four truck tires for every one trailer tire over the years. Come to think of it, I've probably plugged ten off-road tires to every one truck puncture, and the holes in the off-road tires usually take multiple plugs. (The record I've seen in our group is seven plugs to stop the leak and get back to camp.)