I agree, adverse possession is theft. Purchasing a property at a tax sale is perfectly legitimate. Title is withheld for a period of years, varying from state to state, to give the owner a chance to reclaim the property before permanent transfer of the title. That is the only legal squatting that I am aware of. In some cases the
local sheriff is used to evict the tax delinquent owner from the property. Most property sold at tax sales are abandoned. The risk to the purchaser is that the owner can settle the delinquent taxes and pay for improvements before the time limit, as in the case of my cousin. Make sure you pay your taxes and you should be fine (Property tax is not much of a problem in Wyoming).
Most squatters in the US make no claim of ownership, they are just trying to hang out without paying rent or a
mortgage and move on when found out. Unfortunately, squatters are often associated with criminal activities, and rightly so, it being a criminal activity as well.
There is a form of squatting that does have some legal protection, which I am in no way endorsing. Renters facing eviction can often remain on the property for many months before the authorities step in and physically evict them. Renters with rent-to-own options have been able to drag out the legal process for years. There is a rental in my neighborhood that had bad luck three tenants in a row. The landlord only collected rent for 6 months out of 36. He was in the hole over $20,000 with taxes and repairs. I don't pity him, as he is not a good landlord or a good neighbor unless forced to by the city, but he is a good object lesson about the risks of owning rental property.
The Desert Land Act, as currently administered, is a farce. Don't even bother with the paperwork. The BLM will never allow an application under the the Act to proceed, at least that is what I was told by the BLM 30 years ago when I attempted to start the process, and things have gotten much tighter since then.
Unfortunately, the days of cheap desert property ended with the proposed MX Missile
project, also about 30 years ago. Desert property jumped up 5 to 10 times previous value and never went back down, even after the MX project was scrapped. Those prices made it nearly impossible, economically, to develop marginal land for
sustainable agriculture.
An option in Utah is the lease or purchase of School Trust Lands.