I disagree more than I normally disagree about nearly anything.
Analog clock is a total disaster, you can't see anything intuitively. The whole feeling of simplicity/intuition is because we have been taught how to read one since we were small kids. A LOT of effort went into that learning process. It's a complex parser.
Why? What is wrong with analog clock. Basically everything:
1) It does not correspond to the natural day-night cycle at all. It does not have 24 hours like the natural cycle. Two cycles are multiplexed into one actual cycle.
2) In most actual clocks that you can buy, the more significant, larger, better visible hand is minute hand. You don't get any rough idea about the time of the day by looking at the minute hand.
3) The minute hand points to some numbers directly. Great idea, you can accurately read the minutes there? Wrong! The numbers say: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. You have to mentally multiple by five to get the minutes.
4) The small hours hand point to... nothing. The hours scale is missing. Not that it matters, the hours scale is accidentally at the wrong place (as explained above).
5) Want to have a rough idea of time, with a quick glance? No way, you see a graphical mess of two hands forming some kind of geometrical shape which means nothing.
I realize most people have probably forgotten how they had to learn the clock at school (or even before). If you don't remember it, you may think it works intuitively. It doesn't. Instead, we run complex parsers in our heads.
But in the end, time is a number. Just like how many apples John gives to Mary, or your math grade, or how long your penis is. Most of the people (especially >90IQ) handle numbers very intuitively. And this is exactly why the digital clock is so much better. There is no mental load, you directly load the number into your brain.
This is not to say analog is not intuitive. Quite the contrary! Analog panel meters are great; you get the approximate value with a quick glance (say, current 0-10A; are we close to overload or not?). We see good analog meters all the time, as in car speedometers, I have nothing to complain. It goes between minimum and maximum (with no strange 24-to-2x12 wrap-around), you will grasp the approximate speed in a nanosecond's glance, and then you can also read the speed accurately enough nearly as quickly as you do with a digital display.
But the analog clock is a colossally bad example of analog meter, because it's ****ed up beyond all repair. Make it 24 hours and remove the minute hand and I will reconsider.