The quad doesn't drop properly when the throttle is all the way down. When armed, the drone shakes a little bit and continues to do this while hovering.

what components or build do you use? can you post a video of your issue?

one thing you can adjust is "idle speed" in the esc settings, but for some turns some idle is needed. there would be another a feater called "dynamic idle"
pid tuning of your quad is important, cut throttle and get shaky moves, sounds like "propwash". difficult to do interpretation. propwash can be tuned out somehow, also the flght-line can help to hide propwash.