Sorry, I answered without giving enough thought. You are right in your reasoning of course.
Still, I find it confusing to have 2 completely different moments of the day represented by the same number.
In phrases like "After 12 PM on Monday", "Before 12 AM" etc. I always need to think an extra second.
Another example is setting automatic responder on the mail, where I need to rely on 11:59, because the date is selected before the time of day.










So you call them 2 different things. Good. Now imagine doing the same for all the other numbers in between. That is what I get by "speaking 24 hours". And it takes less sillables.