The value is in creating a summary, to collect all the stream of conscience updates into a coherent statement about status and next steps. A daily standup of summaries removes the burden of mentally remembering yesterday's minutiae to reconstruct the current state.

I mean, if you want to know the status of a system do you go to the dashboard or do you go review every system event for the past few hours? I hope not the latter! That's what you do when something seems off, which is exactly the case too for daily standups. If something doesn't seem right, you go review discussions and updates.

Also, at the risk of triggering on standup philosophy, I do believe that zoning out during standups mean it's being done poorly: updates are too long or people are not engaging each other. That's the problem to fix, by setting an example of good habits yourself: cut off rambling, encourage active cross-questioning and ideas, etc.