Ok, so you're a 10-pointer, the mobility agreement is literally the same as the one you had depending on your A school if enlisted or OAIS if an officer. Basically, at the will and judgment of the mysterious system in DC. No different.
Yes, some rather unfortunate souls can be bounced around. Especially if the person comes off as a jerk, front office can go into the personnel system and reassign you which starts a 28 day timer for you to move. Some travelers were done this way, so not quite like a per diem system. Others were used to plug critical holes in the way you imagine.
I have some very non-PC advice on the matter, but basically the PC version of this is to make sure you have the arrangements in hand BEFORE you go into the personnel assignment system to make requests. This really, really helps if you're one of our VALOR interns and can get the right connections to find the right shortages.
If I were you though, I would go this way and apply anyway. 10 pointers get a fairly good shake in the system, and we have rather broad discretion on that matter especially if you have to be stationed somewhere that you need treatment. (For example, one of the residents got a forced match to an SCI medical center because they were unfortunately also an SCI patient of ours.)
And there's only two places in the country with that access. If you're in the West Coast version of that, there's considerations that we can talk in private about as the positions are guarded. If you are in the Southeast Coast version of that, I hope you come from a local school or good luck trying.