Listen, I'll take pretty much any opportunity to bash this organization's management, but IMO, this is not one of those situations where the blame lies solely on their shoulders.
The crowd complaining "Wow our management is so stupid, how come they didn't trade him when his value is high! Now we're going to get nothing in return!" is probably the same crowd that would have complained if he was traded a few seasons back. The problem with trading young players, especially in hockey, is that it is too difficult to determine when their value is going to drop. After DZ's rookie season, I'm sure none of us were expecting this sort of collapse in his game. Hell, even in the beginning of LAST SEASON I thought he was one of our best defensemen (albeit for a short period of time).
Del Zotto plays defense, a position that experiences tons of growing pains and seasons of inconsistency. This is even more applicable for puck moving defensemen. For this reason, it is not only difficult to predict when their value is at its highest, it is also difficult to justify trading them considering they are a necessity for contending teams.
This season though, management has handled him rather poorly. This aspect of his downfall is their fault. There has been no ups and downs in his game this season, he has been consistently poor. If they were going to trade him, they should have either done it quickly (considering his value was going to stabilize) or actually let him play. The act of scratching him consistently over the likes of Falk and Allen will most certainly diminish his value even more. It tells other teams that his play has not only declined, but has gotten so bad that we expect 6th and 7th defensemen to contribute more to the line up than he does.