An analog watch quickly shows the "arc". For a 9 0'clock appointment, my digital watch says it's 9:50, and I have to do the math mentally. My analog watch displays an arc that is faster to interpret.
Either watch display you are late.
You are also aiding the tape/command bug argument. In your case you had to know the appointment was at 09.00. You had a CMD bug in your brain, it was not visible. Thus you had to first identify 09.00 on the clock face, then interpret the current time and visually decide the error. On a tape there is a CMD bug visible, your current parameter is visible and the error is there at a glance. Even on round dials in big jets, in the latter days I flew them, there was a V2 bug & a Vref bug that was set manually. Only in Cherokees etc. did we fly fixed memory speeds in critical phases. True, on B732's the Vfly was about 4-5 O'clock as we flew about the same weight every time, but there was still a bug set; thus there was a visible datum and error arc. One is an arc and the other linear. A common argument is 'the rate of change is more understandable on a dial than a tape'. True, when the dial is unwinding or winding up at very high speed. Neither is common on a passenger jet during normal ops. I wonder what the reaction was when the move from 3 pointer altimeters to a combination of digital and single pinter was made? There is no doubt the latter was a major safety enhancement. Sometimes, with pointers, less is more.
Imagine the old T-scan. You had to interpret the ASI needle, the VSI needle, the Alitmeter needle, and perhaps even a VOR/ADF needle. All were in different 'clock' positions. That is a lot of brain power and skill. Now you can scan/glance across the displays and see if the a/c bug = CMD bug. The brain power required is far less and allows much more time to assess and decide. It allows more time to maintain better SA; it is so much more relaxing and allows a better overview of the operation. Specific errors in all the performance parameters are more evident with less work. What's not to like about that?
I flew B767 in the early days of speed tapes. One a/c we had had both ASI & speed tape; another only speed tape. By luck, or bad luck, I seemed to fly the ASI a/c mostly. I found myself looking at the ASI: old habits. Then I flew the other tape only a/c with an LTC. He took the time & trouble to explain in depth how to use the speed and all that it portrayed. The mists lifted, the fog cleared and I was converted. More importantly I then knew how to teach it myself.
To the sceptics we have to "agree to disagree". To those who say a pilot should be aware of the numbers; I agree, but in a different way perhaps. I know what I expect to see as Vr & V2 and Vref after a calculation; also N1% for takeoff. It's a mental 'gross error' check that I've adopted after years of seeing the computer calculations. If I agree and accept the number then I fly the CMD bug it gives. There is no doubt that this 'gross error' check is not part of the culture of todays cadets. Incidents have happened because of errors that went un-noticed. This opens up a whole other debate about blindly accepting answers from computers/calculators etc. That has been thrashed before, so I do not wish to resurrect it.