Well, for one, public rights of way do exist on, and adjacent to, every public road. But that's kind of besides the point.
I think there's probably many reasons, but here's a few I can think of:
1. The trails and such that warrant these rights never existed in the first place.
2. The rights come from long-established customs, which again, never got the chance to get going in the United States.
3. The legal/juridical establishment in the United States tended to care more about protecting the rights of property owners than protecting the freedom to travel (in this limited respect).
There's a lot of legal history there. The US never had feudalism. The overthrow of feudalism resulted in reduced land rights for large landowners.
There's another amusing historical accident - Blackstone.[1] Blackstone's Commentaries[2] are a self-contained four volume set on how the English legal system worked. They had a strong influence on the US legal system. Most of the drafters of the Constitution read them. There were few if any law libraries, but many copies of Blackstone.
Blackstone was a property rights absolutist. He wrote:
"So great moreover is the regard of the law for private property, that it will not authorize the least violation of it; no, not even for the general good of the whole community. If a new road, for instance, were to be made through the grounds of a private person, it might perhaps be extensively beneficial to the public; but the law permits no man, or set of men, to do this without consent of the owner of the land. In vain may it be urged, that the good of the individual ought to yield to that of the community; for it would be dangerous to allow any private man, or even any public tribunal, to be the judge of this common good, and to decide whether it be expedient or no."[3]
This is further than English law goes. US law arose from that interpretation. That's the power of writing the most widely read book on the subject.
For good reason, one can suppose. Wealth flows downstream from the concept of private property whose rights are strongly guarded by law. An "ideal" amount of property rights, if one exists at all, is likely much closer to absolute than zero.
"(Trespass) signifies no more than an entry on another man’s ground without a lawful authority, and doing some damage, however inconsiderable, to his real property. For the right of meum and tuum, or property, in lands being once established, it follows as a necessary consequence, that this right must be exclusive; that is, that the owner may retain to himself the sole use and occupation of his soil: every entry therefore thereon without the owner’s leave, and especially if contrary to his express order, is a trespass or transgression. The Roman law seem to have made a direct prohibition necessary, in order to constitute this injury: “qui alienum fundum ingreditur, potest a domino, si is praeviderit, prohiberi ne ingrediatur.” But the law of England, justly considering that much inconvenience may happen to the owner, before he has an opportunity to forbid the entry, has carried the point much farther, and has treated every entry upon another’s lands, (unless by the owner’s leave, or in some very particular cases) as an injury or wrong, for satisfaction of which an action of trespass will lie; but determines the quantum of that satisfaction, by considering how far the offense was willful or inadvertent, and by estimating the value of the actual damage sustained."[1]
Except for the carve-out for fox-hunting: "In like manner the common law warrants the hunting of ravenous beasts of prey, as badgers and foxes, in another man’s land; because the destroying such creatures is profitable to the public."
I think there's probably many reasons, but here's a few I can think of:
1. The trails and such that warrant these rights never existed in the first place. 2. The rights come from long-established customs, which again, never got the chance to get going in the United States. 3. The legal/juridical establishment in the United States tended to care more about protecting the rights of property owners than protecting the freedom to travel (in this limited respect).