I do think this would be a cool dynamic to have, and suddenly give purpose to a long existing feature from a gameplay perspective (it obviously always had a use in player communication). It could even be slightly limited, with some Skeletons still running on the "standard" priority they have now, but one or two in the bunch could break off to follow orders issued allowing players to tune the crew a bit and engage more directly with the Burning Blade (and truly feel like they have taken charge of it).
Of course you do have the issue to address of when a Crew has multiple members spamming commands at the same time, potentially conflicting ones. This would likely be more of a problem for an Open Crew, admittedly, but it is something to consider nonetheless.