Well, when someone asks me what time it is now, I don't say, "The minute hand of my watch is pointing at the 1, and the hour hand slightly past the 3." Instead I translate it to "three-oh-five". Wouldn't be too much of a stretch to say 15:05 instead.
(My point being that many watches and clocks already don't give us the literal time as it's spoken, just a representation.)
Edit: although just to be clear, I don't actually think we should switch to a single time zone. It would cause all kinds of headaches. I just think if in some universe it were to happen, it would necessarily go along with a switch to 24h time.
You can say 15:05 because you know it's the afternoon and so 3:05 translates to 15:05. Now think through how that works when the whole world is on a single timezone.
(My point being that many watches and clocks already don't give us the literal time as it's spoken, just a representation.)
Edit: although just to be clear, I don't actually think we should switch to a single time zone. It would cause all kinds of headaches. I just think if in some universe it were to happen, it would necessarily go along with a switch to 24h time.