There are hundreds of these trees around my town. The council seems to just mow over the debris if they are in grass or sweep them up if they are on the roadside.

I don't know about horse chestnuts, but i use a leaf blower for my gum balls. I does a decent job, especially if you cut the grass before they start to fall. If you wait the job becomes a little more difficult as the nut get tangled in the grass.

I suspect I would reach a point where I would hire out this project to a company with a professional lawn vacuum.

I grew up with a horse chesnut tree in the parking area next door. Doesn't a rake pick it up? Don't remember it being any more of a problem then a burr oak or a walnut Rake it into a pile ands coop it into a bag!