If they want to do that to a DH'er then take your time getting off the plane, walk as slowly as you can to baggage claim, go get a coffee, stand in line for security, proceed to the gate, and get the jet ready. If you take a delay you can tell dispatch that if you didn't have to go out and get your work items from baggage claim then you might actually have made the departure time. Enough of that and the company will change that policy!