Funny you should use 15:39 as your example.

I find the translation I have to do from 15:39 to 3:39 pm to have much more friction than reading a digital or analog clock in the first place, both of which I can do with equal ease.

The problem of course is that I'm not used to 24-hour times, so I don't equate 15 with any particular time of day. Similar to how I have to translate C to F to make sense of C temperatures.

Now, a 24-hour analog clock with an embedded digital temperature read-out in C, that would really hurt.

Apparently 24-hour analog clocks are thing:

https://www.amazon.com/Navaris-Hour-Wall-Clock-Non-Ticking/d...

Ouch.