No, my thinking was not that far. I was just wondering if others agree that this metric would be useful. Seems the answer to that is yes. Putting it as an info the diagnose mode makes certainly sense. Putting it as well into the startup message from cmdstan may also make sense for the reason you mention, Bob.
The issue with making this number show up by default is that it is very technical and most users will simply be confused by this number. On the other hand this is message will come as an information and as such may just trigger interest from the user to read about this a bit more in the manual, which would be a good thing.
Maybe we have a short discussion on our next meeting on this?
Personally, I would find it interesting to see the scaling of the AD stack size with the problem size for a given model (which I would have to script myself once this feature is available, of course).