Another issue with the conventional format is that tasks or workstreams aren't discussed coherently; instead, each subject comes up briefly depending on the order in which team members speak. This can make it hard to tell what's really going on.
I've experienced these phenomena on projects of medium scope in large enterprises. It seemed to me that the scrum-of-scrums approach worked well provided there weren't enough teams to require more than one level of depth. We started to have logistical problems and communication break-downs once the overall project size reached roughly 25 - 30 people, divided into agile-sized teams. Proponents of the scrum-of-scrums approach say it scales linearly, but in my experience it has not done so. Instead, the relative amount of overhead to manage the meetings seems to increase with the depth of scrum-of-scrums meetings. Teams that need information about other teams seem to be pushed farther and farther away by this structure, too, and we start to experience some of the same sorts of communication problems as we did in the pre-agile days, when most communication was indirect.
The other day, I set up a task board for an XP team I'm coaching. They had been using an electronic tool to track their backlog, since that is necessary for remote collaboration. They had been using the conventional format for the daily stand-up. I got the sense that people were not quite sure about the status of each story or about any blocks their teammates were experiencing. The first day they gathered around the task board, which reflected the status of the iteration as it existed in the electronic tool at the time, they immediately started to walk the board instead of following the "three questions" format. I found it interesting that this happened organically and without any prompting. They very quickly and effectively communicated the status of everything and moved cards around to reflect their individual understanding of status and issues, resulting in a more up-to-date reflection of the project than one could find in the electronic tool. They also identified blocks and took ownership of them, naturally and without any prompting.
Some of the team's stakeholders are local, and when they noticed the unusual activity they wandered over to see what it was all about. They also related to the task board immediately and naturally, having received no training and no explanation of any kind about what the board meant. They could see exactly what was holding up progress on individual work items, and were ready to take action to remove barriers.
To me, this was a beautiful example of the power of information radiators and also of self-organization. Before I set up the task board (it consists of sticky index cards on a window; nothing fancy), people discussed the idea of a task board in the abstract, and were not able to visualize how it could help them. They saw keeping the board up to date as "duplicate work," since they already used an electronic tool for the same purpose. They had to experience the task board before they could really understand how it could help them. Now they use both the tactile task board and the electronic tool. They are beginning to see the electronic tool as a mechanism to share the information from the task board with remote stakeholders, rather than as the primary tool for tracking the work.
The other interesting thing is that the team automatically fell into the "walk the task board" form of the daily stand-up. They didn't bother to take turns answering the "three questions." I noticed this, of course, and observed them to see what they would do. Afterward, I asked them how they felt about the way the stand-up had gone. They said it seemed more effective to walk the board rather than answer the three questions. This is not a large team; it has seven members, the ideal agile team size. Even at this size, the team got value from the alternative approach to the daily stand-up. So, it can be seen as a practical demonstration that Corey's approach to the daily stand-up works for small teams as well as large ones.
Some teams may want to consider this approach to the daily stand-up. There's more than one way to solve a problem, and in some cases this approach may be more appropriate than the three questions.