I’m sorry but it doesn’t make sense to me. Regardless of the month, I think what matters first is to know what day of the month you are in, if at the beginning, in the middle or at the end of said month. After you know that, you can find out the month to know where you are in the year.
What is the benefit of doing it the other way around?
I’m a fan of the 01JUN2025 format. It’s unambiguous and uses about the same space as other traditional formats.
It’s how I was taught in the Navy to write dates. I stood a lot of watches and made a lot of log entries.