If the girls have a proper sequence they will not drop their hands. IMO the cue "don't drop your hands" or "keep your hands up" is wrecking havoc with the sequence and actually causing kids to drop their hands at swing initiation.
IMO the absolute easiest way to solve the issue of kids dropping their hands at swing initiation, is to let the kids drop their hands...cock their hands...as they cock their hips. The hand cock is a natural movement that keeps the hands in sync with the lower body when the hips are cocked. The hand cock is what allows the stretch part of the sequence to happen naturally. If you eliminate the hand cock then you need to come up with drills to teach the kids how to perform the stretch part of the sequence unnaturally.
Ignore the green arrow.
The hand cock takes on a different appearance depending on the batting stance handset. IOW, there are different hand cock styles. IMO one of the worst things you can do is tell a kid to keep their hands up; which is the same thing as telling them to keep their hands still; when they perform their hip cock.
Agree that the issue of dropping the hands at swing initiation is generally the result of an improper sequence.
You mentioned about allowing hitters to drop their hands ... and I agree with that as well ... I even teach it with hitters that experience timing related issues in their loading pattern. To clarify, you meant as in a 'hitch' ... on their way to launch ... and it generally leads to a well timed "up & IN" action ... I want that well-timed "up & IN".