One advantage of double triggers, beyond those already mentioned (which are substantial) is that with two triggers you have instant choice of barrels, and , if you choose to do so, you can load one solid, one soft point, giving you instant access to the proper bullet for any occasion (if you can remember which is which).

The shotgun barrels of my double rifle/shotgun set are choked differently, so I also have instant access to either choke, and it's great practice for manipulating two triggers.