Chris, I respect your knowledge and experience.
The tandem axle, dual wheeled trailer shown has 4 sets of bearings and 4 sets of brakes. It also has 4 leaf springs, 4 leaf spring main pins and 2 equalizers to maintain/grease.
The triple axle trailers I have seen have 6 sets of bearings and 6 sets of brakes. They also have 6 leaf springs, 6 leaf spring main pins and 4 equalizers to maintain/grease.
The triple axle single tire trailer does have an advantage of only having 6 tires to maintain. But doesn't that also increase the load on each of those tires over the same load being carried by 8 tires of a dually??
As for changing a tire, as discussed above, no difference. Still gotta jack up an axle and remove 8 nuts. And also as stated above you have the other dual to hopefully carry the load to a safe spot for repairs. Which I've had happen when an outer blew going 70 mph on a busy 4 lane hiway.
Lastly, I cringe every time I see a triple axle doing a sharp turn with a load. Very hard on tires, hubs, wheels, etc.
Again, with all due respect, I'll stick with a dual wheeled tandem setup. The OP stole that trailer.