Actually, I've seen the use of 24:00, as well as 25:00 and 26:00 and 27:00 to indicate late night 1am, 2am, and 3am the next day. I've seen this on TV schedules as well as train/subway schedules in some countries. Although these times don't actually exist, what is meant is well understood and causes less confusion in general. For example, if train depart at 25:00 Monday, it's intuitive that it's late Monday night. If it's specified as 01:00 Tuesday, some people will not realize that this really means late Monday night.

I think it especially makes sense in the case where what is being referred to does not operate all night long. For example, if a subway system operates from 5am - 1am daily, then having the departures that depart between 12am and 1am are more intuitive if they are listed as 24:00-25:00 the previous day, especially if there are ticketing standards such as a "single-day unlimited pass" which treats the final 12am-1am hour as part of the previous day.