I'm actually surprised there is so much of it. If you are talking about asphalt roads, most of us try to ride alongside them since they are hard on our horse's limbs. Even gravel roads are hard on the hooves, so we usually stay at the sides if possible.
In many more populated areas where I live, like subdivisions, there already restrictions that apply. Also, most parks don't allow horses, and most forest preserves only allow them in designated areas, if at all. While horse manure is biodegradable and can be spread and composted to function as fertilizer, piles of raw manure don't function that way, and they do smell and will attract disease-carrying flies and harbor their larvae.
I don't leave piles of manure in my driveway or in and around my barn. So I don't think it is all that unreasonable to not like having it all over the roads. The problem is that it just isn't practical or even safe to clean it up while you are riding the horse.
My fear is that riding may be increasingly banned along the roads if people don't listen to what you are saying. I would advise people to ride along the sides of the roads whenever possible, to avoid this becoming an issue with the public at large who drive on the roads and who don't care whether horse manure is less toxic than dog manure, From their perspective, hitting a big pile is noticable, and they don't want it on their tires because it packs into the tread, it gets slung up into the wheel wells and onto the paint, and it stinks.
And, unfortunately, the fact is that horse manure certainly can and does contain organisms that are harmful to humans, including bacteria like E. Coli, Listeria, Salmonella. Clostridium tetani, and protozoa like Giardia and Cryptosporidium.
When it comes to issues like this, those of us who ride horses need to realize that we are in the minority, so we need to do what we can to avoid being labeled as any kind of public nuisance if we hope to maintain the right to ride our horses along the public roads. I've already seen it banned in many places during my lifetime. More recently I've seen horses banned from most or all of the bike paths and walk paths, largely due to the problem of dealing with the manure.
We can sing the praises of horse manure until the cows come home, but I doubt we'll convince anyone but us horse owners to embrace it. And in most places, we don't represent the majority interest. So I just hope we don't continue to lose the right to ride in public areas such as along the roads because of these kinds of issues.
57 years with horses