If the trailer is very light in comparison to the load rating of the tire then doing so would result in uneven tire wear. But your statement is correct in that the tire will handle higher speeds at the higher PSI, until the tread wears badly in the center!
This is often stated, but in my experience on my trailers, not true. I am running four trailers currently, all of them with over-spec'd tires for the load. All run at max sidewall pressure. Three of these trailers run LR E tires at 80psi, and this travel trailer I'm sitting in has LR D Kumho 857's on it. I am running at less than 50% of the rated load of the tires. Inflated to 65 psi, they now have right at 40,000 miles on them. Wearing exactly even, and about one third of the tread gone.
That's my experience with it. For trailer use, especially tandem axle ( all of mine ) I prefer max sidewall pressure.