I would say; why choose. Now in 2020 internationalisation is old hat. So just show whatever date format the users browser says they want.
My understanding is that Stack Exchange sites are build in C# ASP.net. ASP.net is very able to pull the users preferred language out of the data sent from the browser and C# is very able to format a date time in that cultures preferred data format.
The current date format regularly causes confusion, as seen in these posts:
Show the whole date, even for posts from the current year
Why inaccurate ''member for" info is shown in Stack Overflow
Don't use very old posts for audits
Allow users to set custom date formats
This would mean American users can continue to use their preferred date format of MMM DD 'YY and non American users would feel a little less unloved.
(The current behaviour of showing a UTC timestamp on hover is good, I'd suggest keeping that)