[0] [12:00 PM, 12:00 AM) for after the noon instant
[1] [12:00 AM, 12:00 PM) for before the noon instant
24-hour time is superior to the mod-12 time system in almost every way but mechanical clock faces and soldier shifts under early systems that used sun dials. However, the equivalent question can be asked by a day is a clopen interval of [00:00 current day, 00:00 next day)
A place open 24 hours/day is open in the period 0-24.
I think you get the essential utility you want in a 24 hour clock by simply letting 24 (or "24:00:00" when fully written out) be a way to represent the end of the day.
It's also already in use, with examples at https://ioi2023.hu/faq/ , http://www.garageferrarimilazzo.com/en/ , and https://jozsefvaros.hu/english/news-in-the-district/2022/12/... .
When is dinner?
- It's at seven.
When does the flight depart?
- At 19:00
No, we don't. The only person I know who by default uses 12h is my grandmother. Everybody else always uses 24h.
All my experience has also been using 12h time in casual situations in 24h countries. I'm curious of a country that doesn't, and whether that's true of the whole region.
I do enjoy though where systems have to deal with 'weird' days. I believe in the UK the rail ticketing system works on essentially a 26h day - that is to say if you buy a ticket at on 5th November, it will be valid until 04:00 on 6th November, so in some sense the hours 00:00-04:00 belong to both days.
Trying to find the source again but not having success.
Bias. Most people can. I'm in the UK, too.
I personally enjoy using 24-hour clocks on all devices I can.
Use of either mechanical displays or on computers time selecter widgets does mean that 24 is not shown anywhere,
You're right that by convention noon is assigned a pm tag and midnight is assigned an am tag. But midnight, when the calendar date changes, is confusing enough to people that e.g. airplane departures will be scheduled for 11:59 pm rather than 12:00 am, because there's no ambiguity about when 11:59 pm will happen on Wednesday, whereas it isn't clear when midnight will happen on Wednesday -- technically, if it's Wednesday, midnight already happened on Tuesday night.
It is far more common for people to end their personal day after midnight than it is to begin it before midnight, so the convention directly contradicts the way pretty much everyone views "the day".
It can obviously be learned, but it's something lots of people have trouble with. I was probably in my teens before I finally got that memorized enough to keep them straight. Lots of things happen at 11:59 PM (due dates being the most prominent example) because it's less potentially ambiguous than 12:00 AM the next day, even though it's functionally the same thing.
Noon is also not "12:00" - it is the infinitely small moment at the strike of 12:00. Instantaneously it becomes post-meridiem. 12:00:00.0000000000000000000000000000001 is after noon.