Lower to the ground is better for anything going down the road as it reduces drag and lowers the center of gravity. You could find your mpg a bit worse too. I wouldn't raise it "just because".
We are probably as high off the ground as they make TTs. We have underslung axles and spring hangers that are 6" tall (not the 4" ones). Tows just fine. We have a 4x4 though, so it's higher height off the ground works well with the taller TT.
One big reason some trailers are made with underslung axles and taller spring hangers is so that the wheel wells don't intrude into the floor space and interfere with things, esp. slideouts.
If you make your trailer higher off the ground, your steps will need replacing with ones with another step. You *could* even find the extra step to be somewhat annoying.
If you have money to spend and want to improve handling, install shock absorbers. We did earlier this year and just had over a 300 mile run last week on some pretty winding, rough and up/down, bouncy roads. I simply can't describe how much of an improvement it's made.