The main positives of an analog clock revolve around how it visualizes time time relative to other parts of the day.
When the hour hand is on 9, you can see at a glance it is two hours from 11 and three hours from 12 without needing to do the calculation in your head. When the hour hand is in the upper right, you know is it shortly after noon or midnight depending on how bright it is outside. When looking at the minute hand, if you see something started at 2:10 you don't need to remember the exact time, just where the minute hand was when you started and estimating being half or a third done until 3:10 is pretty easy. 15 minutes is easy to figure out because it is a quarter of the circle.
It conveys this at a glance without needing to focus so much on the exact hour or minute. Visualizing our time results in thinking about how we are using our time.
Like anything else, that doesn't make it superior in every situation and they suffered from constantly being out of sync with each other by a few minutes or seconds.