It should be noted that the "round robin" format has an important aspect which is to enable each team member to air his/her personal grievances regarding anything related to the project.
"Worked on adding discounts to the shopping cart page. Went over to talk to Chris in billing about that, and he mentioned in passing that they are planning to move on to SAP next year."
That could be incredibly important information for the team! It doesn't come up as naturally when working through stories as in a round robin.
That mindset is precisely the reason why these meetings are important, because these grievances might not necessarily reflect or deserve a ticket. They might be nothing or they might be something. What's important is that these meetings create a space where they can safely be addressed without creating any burden on the team and on the individual reporting them.
I've read somewhere that these meetings work as therapy for the team. Perhaps by putting it this way you might better understand the issues these meetings solve.
That doesn't cut it. Being expected to talk about stuff doesn't put you on the spot, and purposely requesting the team to address a concern makes you stand out as the one creating problems where none existed.