It's written both ways in the US. Most people write the month first, while some others the day first. For example, sometimes I write 7 April, 2022 (for today). As long as you write the month (January, Feb., etc.,) there won't be any problem.
That substitutes one issue for another.
The months are straightforward enough until there is a change of language.
For example, if a Greek monoglot wrote a date using that convention, I would find it awkward to work out the month.
Ιανουάριος (Ιαν, Ι) – Ianouarios.
Φεβρουάριος (Φεβ, Φ) – Fevouarios.
Μάρτιος (Μάρ, Μ) – Martios.
Απρίλιος (Απρ, Α) – Aprilios.
Μάιος (Μάι, Μ) – Maios.
Ιούνιος (Ιούν, Ι) – Iounios.
Ιούλιος (Ιούλ, Ι) – Ioulios.
Αύγουστος (Αύγ, Α) – Avgoustos.
Σεπτέμβριος (Σεπ, Σ) – Septemvrios
Οκτώβριος (Οκτ, Ο) – Oktovrios
Νοέμβριος (Νοέ, Ν) – Noemvrios
Δεκέμβριος (Δεκ, Δ) – Thekemvrios
Yes, I'd get there with Roman letters, and might eventually manage with Greek letters. But Greek is easier than, say, Japanese.
Pure numeric avoids the language barrier. I prefer yyyy/mm/dd because it would be perverse for anyone to use yyyy/dd/mm. Therefore, it is safe enough to assume the format.