This is still a partial solution as the user needs to know that their locale is being used and know how their locale is configured to understand the format. This is most problematic on shared computers or kiosks, especially when traveling.
I mean, once in a different country, you either experience the locale shock once then adapt, or you've seen it before and kind of know what to expect.
And for the rest of the users who have no idea about locales, using whatever locale they have on their computer might be technically incorrect for some of them, but at least they're somewhat used to that incorrectness already, as it's likely been their locale for a while and will remain so.
I don't even know my locale.
Is is the device display language, the keyboard input language, my geo location, my browser language, my legal location, my browser-preferred website language, the language I set last time, the language of the domain (looking at amazon.co.uk), the language that was auto-selected last time for me on mobile or... something else entirely?