From a real-world perspective, I suspect that the headskirts were originally created to avoid creating a full head prosthetic for guest actors. Once the character of Quark was created, the cost of a reusable full head prosthetic would have been less prohibitive.
Your suspicion is correct. Several behind the scenes videos and past producers have confirmed this as the main reason. Not only cost, but time needed to do the full head makeup.
Neat! I’ll definitely check this out.