Well I think it was me that suggested that the law was messed up, so don't take offense at my statement. I understand your desire that the rules were different, but unfortunately they are not.
BLM doesn't sell land within their boundries (at least not yet), so that is not a question in this issue. What they attempt to do is obtain all the land within their boundries. Fortunately the law won't allow them to use eminate domain to just sieze it, so they attempt to negotiate with the land owners to take control of the land. This may include trading for land on the edge of the BLM "bubble", thereby making the BLM property the same size, and at the same time excluding private property in the middle of it, or it may include the outright purchase of the land from the property owner which increases the size of the bubble while still excluding private property in the middle of it.
There's nothing that says that these property owners have to give up their land (yet), however the law does mandate that the property owner be given easement rights to be able to ingress and egress their private property. Nobody else has the rights to use that property other than the landowner(s) that use it to access their property.
I only assume that the law is written this way because the landowners are 100% responsible for maintaining the private easement, and the BLM charges you a one time fee to obtain the easement. BLM doesn't come in and pave a road to your property. They just say, OK, here's a 10' wide swatch of land that you and only you are allowed to use so you can get to your property from the nearest public road. You have to take down trees, grade it, gravel or pave it at your own expense, and it is in the purest form a private road.
I own 6.5 acres two miles inside BLM controlled national forest, and I'm sort of familiar with this topic from the numerous conversations I've had with BLM over the years. I'm not an ass that tells people that they can't use my driveway to access areas of the forest beyond my house, but I can easily see how I would get annoyed if my carport became a parking lot for trailers full of ATV's. I don't have a fence or a no trespassing sign on my place, but I'm fully entitled to put one up if it were to become a problem.