Desynth makes me think of a new DoH class to be added:
Salvager
*Breaks down finished equipment
*Weilds a wrench MH, screwdriver OH
*Ignores class requirement when repairing gear
*Can attempt repairs 5 ranks sooner than other classes
Breaking down equipment would not give shards. If desynthing yielded basic mats that wouldn't help the bigger problem since items are not exiting the market. Only thing I can suggest would be that desynthing gives a new material called Salvage. There could be various types and rarities depending on the optimal rank and base components of the item being broken down. Just have to find a use for Salvage then (besides being a universal repair material).
Reminds me of Cid from FFIV ^^