Meanwhile the advantage of day first is that often you don’t need to say the rest since if you don’t it’s implied as the present one (i.e. if I tell you now “let’s have that meeting on the 10th” June and 2024 are implied) so you can convey the same infomation with less words (however in written form meant to preserve the date for future reference you have to write the whole thing anyway)

That advantage is not exclusive to the date-first system. You can still leave out implied information with month-first as well.

Personally I recognize that it’s mainly familiarity that makes me favour one format over the other and logically I don’t think one way is overall better than the other one as the advantages of each are situational.

This is the biggest part of it. No one wants to change what they know. I’m from the US and moved to the UK, and interact with continental Europeans on a daily basis. I’ve seen and used both systems day to day. But when I approach this question, my answer isn’t “this one is better because that’s the one I like or I’m most comfortable with”, my answer is “if no one knew any system right now, and we all had to choose between one of the two options, which one is the more sensible option?”

dd-mm-yyyy has no benefit over yyyy-mm-dd, while yyyy-mm-dd does have benefits over dd-mm-yyyy. The choice is easy.