I like international standardization, but I like unambiguous process and product control much more.
DD MMM YYYY helps you check it...incorrect use is obvious in most cases. It's also self-reminding to the user.
ISO 8601 is not self obvious to users, especially those that have spent decades using other all-number formats with different orders. 8601 can be used incorrectly during days 01 through 12 without that error being obvious.
I'm sympathetic to the language challenges involved, but I'm unwilling to accept uncertain product and process control as a cost of solving those language challenges.