Which makes a lot of sense, the 4th amendment was never meant to protect land this way, It was always meant for personal things and the household, not meant to carve all private land as off-limits to everyone and the government.
In regard to access to land, I really like the Freedom to roam [0] doctrines of a few European countries.
This instance seems like a 'taking'. The government should have to pay rent if the installation is more than transient (something like 24 hours), and they should not be able to keep it secret from, or disrupt the owner's use of the land without invoking eminent domain.
You are making a rather basic, fundamental, and common mistake due to modern eroded understanding of language and meanings. The effects that the fourth amendment prohibits the government from violating, do in fact include land property.
The Rights of Way in say the UK are way older than your or anyone's farm. They are a form of returning back to the Commons that which was always part of the Commons. It's rather more complicated than that but that captures the general spirit of Freedom to Roam.
Some of the roads and tracks hereabouts are quite old. Many are rather older than written evidence. For example the Sweet Track (1) up the road from here is getting on a bit. I'm not sure if it still counts as a Right of Way as its a Scheduled Monument!
I live near to the Fosse Way (2) which is a bit more modern - a Roman road. Quite a few of the roads hereabouts are still called "Roman Road" which is surprisingly unimaginative. The county of Somerset is quite well known in the UK for having an above average of really odd place names, which is quite a boast, given the competition.
I imagine that you live in a land that can cram several UK land areas into one state. You may like your seclusion but I hope it doesn't belong to someone else 8) Provided trespassers errr ramblers keep their dogs away from your livestock and close gates and don't litter then all is good. To mitigate some of the side effects of rambling we have a few laws. A farmer has some legal protection when a dog attacks their livestock (3) Erm, I've just read the Act and it looks like only a minor fine. However, anecdotally, dogs worrying say sheep sometimes don't survive the encounter. I'm a massive dog lover (there are five in the room here) but they can't be allowed to worry livestock. We also have stiles, routinely provided to get over walls and hedges and cattle grids for similar reasons but mainly for roads.
Bear in mind that you too are a common person and your rights are probably protected by a form of Common Law - don't knock it and I imagine that you might have one of those new fangled Constitution things spelling out your Rights too. A Bill of Rights plus documented Amendments is quite a handy thing to have around. You could "take the fifth", I'd need a lawyer to even try to do a similar thing and I think that here in the UK "it may harm your defence if you choose to not say something that you later rely on in court".
In regard to access to land, I really like the Freedom to roam [0] doctrines of a few European countries.
[0] https://en.wikipedia.org/wiki/Freedom_to_roam