While most of this is valid (how dare a space opera expect me to suspend disbelief!), I think there is a basis for such a compactor to exist in the first place.

It stands to reason that a smaller vessel like a Star Destroyer, it is not logistically challenging to move the trash to an airlock for ejection.

On something so enormous as the Death Star, however, it might be so difficult to move the trash around that it's significantly more efficient to compact it before transport to the surface.