The minimal or non-existent benefits for most people in most situation of yyyy-mm-dd (no, the brain doesn't need the highest dimensional scale value to come first: that's just your own habit because of how numbers are spoken in the English language and possibly because the kind of situation where you use dates involves many things which are further than a year forwards or backwards in time, which for most people is unusual) - people sorting dates by alphabetical order in computer systems (which is where yyyy-mm-yy is the only one that works well) is just the product of either programmer laziness or people misusing text fields for dates - so don't add to enough to justify the "jarring" for other people due to changing from the date format they're used to, not the mention the costs in anything from having to change existing computer systems to having to redesign and print new paper forms with fill-in data fields with a different order.

In a similar logic, the benefits of dd-mm-yyyy are mainly the ease of shortenning it in spoken language (i.e. just the day, or just the day and month) and depend on knowing the month and year of when a shortenned date was used (which usually doesn't work well for anything but immediate transfer of information as the month and day would still need to be store somewhere if they're not coming from "present date") so they too do not justify the "jarring" for other people due to changing from the date format they're used to.

Frankly even in an imaginary situation were we would be starting from scratch and had to pick one, I don't know which one would be better since they both have flawed advantages - year first only really being advantageous for allowing misusing of text data fields or programmer laziness in computer systems whilst day first only being advantageous in immediate transfer of date information where it gives the possibility of using a shortenned date, something which is but a tiny gain in terms of time or, if in a computers system or written form, storage space.

It's really not a hill worth dying on and I only answered your point because you seemed to be confusing how comfortable it felt for you to use one or the other - a comfort which derives from familiarization - with there being some kind of general cognitive advantage for using any order (which, in my experience, there is not).