If Daisy was also on the offense, they'd probably end the game faster. I don't see any reason to leave her behind since as you said, she's one of the wreaths. She can defend herself. Just leaving her behind just reduces the Millifiore's offense and imo, is in a way, looking down/underestimating the Vongola.
Irie running our of flame = game over. So it's not really them having a commander or not. lol