I grew up with DD.MM.YYYY. But I think, MM/DD makes sense in everyday usage. You don’t often need to specify dates with year accuracy. “Jane’s prom is on 7th September” – it’s obvious which year is meant. Then it’s sensible to start with the larger unit, MM, instead of DD.
Even in writing you see that the year is always given like an afterthought: “7th September**,** 2023“.