I'm struggling with that response from Tredit - do not see how loading affects tire balance. It affects wheel track (alignment) at the suspension shifts, but balance is balance regardless. However, it still may be true that balance has little positive effect on trailer tire life.
Also, small (i.e. light) tires don't suffer much from balance issues and a lot of what Tredit is talking about is probably 8" or 12" wheels with relatively skinny tires. Small diameter, low mass, tires/wheels simply don't generate a lot of force even if a bit off balance. With larger RV trailers, though, some of the tires are substantial, 16" wheel and wide, and have a bigger effect (more energy).
A badly out-of-balance tire is going to shake things, but I think that is pretty rare on trailers. Rare doesn't mean never, of course. I've seen a very few that were obviously way off balance. The lack of shock absorbers on most trailers is probably a much larger factor, though.