There have been studies for decades on overhead hay racks for horses and cattle which found pretty much the same thing. The dust gets into the eyes and nostrils of the animals and causes nasty problems.
If you think about how a particular animal eats when it's in a natural environment, you can see the way nature intends for the animal to eat. With horses and cattle, it's almost pure grazing on the ground. Sheep, too, of course. With rabbits it's grazing on the ground level, with the occasional reach upwards for fruit, as well as gnawing of tree bark at nose level.
I've been using a piece of cage wire bent into a J shape attached on the outside of the cage for a couple of the bunnies. It's attached to the hole that a J-feeder would go into. They pull the hay in quite easily. This is for timothy. The alfalfa I still feed on the floor or in a pan on the floor because I want to give them the ability to snarf up the leaves that fall off if they want them.