Milpers don't HAVE to move around so much. The civilians have about as much effect on the morale of the qualified uniforms as do homosexuals having been placed atop a pedestal as some honored species.
You have overseas billets that have to be filled. These posts are filled by active duty. The civilian slots overseas are few and far between.
Active duty are subject to deployments. Only some civilians are deployable and it’s usually voluntary.
Your idea about the effect of civilians on morale is twisted. Civilians are a small fraction of the work force at most bases. Some bases your backbone is all civilian. Some civilians can be pains just like some military.
When an entire unit deploys, the civilians are the ones who keep the home station mission running.