Does the concept of meetings without agendas seem counter-intuitive and against just about everything we've been told about good meetings and making use of our time efficiently?

Maybe there's another way, as described in this article.  Use the power of your team to reach a consensus of what is best accomplished in the time you have available.

Being prepared is good, but sometimes no preparation can lead to a beneficial outcome. This is something new to use to help drive the organization forward.