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You are mostly right, but I wanted to correct a few details. BLM grazing permits, or more accurately preference, can be marketed independently of the base property. This is a common practice. The buyer of the preference must meet the requirements of holding a grazing permit and one of those is base property. The preference is easily, and often, transferred from one base property to the next. Some permittees transfer their permits between different properties they own or they can be transferred to the property owned by someone else. It's a bit different for USFS grazing permits as they are tied to the livestock herd and not to property IIRC.
Similarly, the base property no longer has to provide the forage to feed the livestock for the time they are not permitted on BLM lands. The basic reasoning for this is twofold; 1. feed can be hauled to the livestock even if they are on a parking lot and 2. the act of calculating forage production on private property by the BLM had the ability to affect a property's value. So, yes, base property is still required to hold a BLM grazing permit, but it no longer has to be reciprocal.
Permits can be taken away for non-use if that occurs, without BLM approval, for I think 3 years. However, if non-use is approved by the authorized officer it can go on for a long time! The Grand Canyon Trusts has held permits for a long time that they make no use of, but since it's been approved they still hold the permit. Any amount of non-use can be applied for by anyone else meeting the requirements of holding a grazing permit, though this is very rarely granted.
