There are other reasons. Speaking from someone who's going through a departmental restructuring, often what you call "lacking common sense" is deliberate and not exactly what you think. They want to get rid of people like you, and if you don't stay, it means the job is not meant for someone like you. For example, they might want to reserve space for their researchers to take a certain %FTE, or outsource their non-profitable ER work to PTers for cheap. Point being, unless you are a revenue center rather than cost center, there's no incentive for the institution to keep you, and instead of firing you outright (and having to deal with ramifications of that), they can create bizarre arrangements as you described and basically force you to leave. You could negotiate, but it's not a guaranteed win, since in general until at very senior levels, what you can provide is hardly unique.
Institutions that employ you, especially in America, are never on your side. At best, there are interests that are incidentally aligned. At worst, your relationships are entirely instrumental. Your position would change if you OWN a part of the institution rather than being an employee (e.g. equity partner at a practice, or tenured professor at a university, or hold an endowed chair position, etc).
