Recently, though, I witnessed a standup meeting dysfunction that was completely new to me - a team member said his piece, waited a minute or so, and then walked away.
First, I was shocked that he did this, but I was even more shocked by the fact that not one other team member questioned his action. Other than the ScrumMaster, I don't think many people noticed. I suspect that the root cause of this problem is that the person in question feels that the Standup Meeting is simply for giving his status.
Providing your status is indeed one aspect of the Standup Meeting, but it is by no means the only reason why you attend. The Standup is intended as a daily synchronisation point for all team members, and I do extend that to include Product Owners. I tell teams I coach that while perhaps 80% of what's said in the Standup may not affect any one individual on the team, the other 20% is absolutely crucial to ensuring that every is working together. Hearing that someone has an impediment may trigger someone to say, "Oh, I had that problem before and fixed it by...". It may make clear the need for a conversation to take place.
Regardless, if you keep the Standup restricted to the 3 questions then it will move quite quickly and that 80% won't feel like much of a waste of time.