Cutting the sugar leaves allows moisture to leave the "core" of the bud, which speeds up the drying process. You do not want to speed up the process. Drying too quickly kills the scent, not completely, but the "nose" won't be as "loud".
Waiting to trim the sugar leaves dry allows the buds to retain proper moisture/oil levels to continue the cure. Drying quick and releasing the moisture/oils ends the cure abruptly and it will not continue if you "rejuvenate" them by increasing humidity.
Though it has been cut down, the plant is still trying to survive. The more cuts you make around the buds is subjecting that area to additional stress. Varying trim methods can yield visable differences in the final product.
Botrytis does not need to start inside of dense buds, it will violently attack any "damaged" areas of the plant. Every cut leaf, then, is a prime target and invites the onset of the disease.
Better "nose", better cure (vs potentially "no cure"), better product, and less prone to Bud Rot. Pretty strong argument for dry trim.