You may see it as being "privileged", others are going to see it as a major annoyance. Most BRDs have little to no skill at Performance.

You're not in the duty to Perform, you're there to kill things. All that would be accomplished is getting BRDs vote-kicked at the first possible opportunity because the rest of the party is there to clear the duty, not listen to a slacker giving a grade school level music recital.

Being someone who does play BRD on occasion in instances, I'd prefer not being subjected to vote kicks because other BRDs want to force their random musical wanderings on parties in a duty.

If you need to play for others, keep it to Limsa or Gridania. Or maybe try Ul'dah, I almost never see BRDs performing at the Aetheryte there.