But, OP says that they are noisy when holding still (hard to believe) and consume current (easy to believe). So detaching and powering off would address both of those issues.
But that most likely is treating the symptom rather then the cause. A R/C servo with proper power (and filtering), proper positioning coding and properly sized to whatever load they are attached to is perfectly capable of not jittering. If you have ever seen the precision that competition R/C acrobatic fliers work at you can see that noisy servos would not be tolerated. There is always the possibility that the OP has very low quality or defective servos, there are some awful cheap models made and sold these days. Wear or missing teeth in the gear train can cause all sort of havoc in this regard. Unbalanced or mechanical overloading is also a possibility. Power is often a root cause.
I guess I just see detach command as a solution looking for a problem, and most often applied for the wrong reasons.
Lefty