I'm not arguing for the inherent superiority of am/pm notation, but I do get frustrated with people who use 24-hour time because "it's more logical", without seeming to realize that it's more difficult for the majority of people to understand.
Depends where / with who you work? Most of my colleagues have to think the same way about am / pm and often get it wrong when it's 12:00 am/pm.
The 'it's more logical' for me does apply there; in the 24:00 you cannot get 12:00 or 00:00 wrong no matter how you think about it. It feels intuitive in every way.
12 hour clocks made sense when clocks had 12 hours on them; then you had to somehow indicate which block of 12 hours; that problem was fixed before I (and probably you) were born though.
Literally, the mnemonic I use to remember which is which is "it's the one that doesn't make sense".
So 11am then 12pm
And 11pm then 12am
(Whereas I would expect the 12th hour of the morning to follow the 11th of the morning, but it's actually the other way around)
I can take it as a "con" against any new system, but it doesn't outweigh all other benefits- if it did then there'd be no progression in society -ever-
I've used 24 hour clocks all my life and everyone uses 1-12 when talking. If someone is coming to see you at 14:00 they will say: "see you at two". We only use the proper format when writing.
Extends obviously to "fourteen thirty".
(Northern England)
In many locales where the 24 hour clock is used, people refer to the hours after noon as one, two, three o'clock etc. Then when you write it down somewhere two o'clock becomes 14:00.
OP's pet peeve is kind of weird though. Even with a 24 hour clock writing 9:00 for 'nine in the morning' without the leading zero is quite common, if not prevalent.
They say "today at noon, Chicago time." Or "9am Los Angeles."
It's become so habitual that they'll even use a city name without thinking if they need to. For example, saying "4pm Biloxi time" to someone in Chicago, which is the same time. But at least it eliminates any ambiguity.