Except that DDMMYY has the huge ambiguity
issue of people potentially interpreting it as
MMDDYY.
Yes and YYYY-MM-DD can potentially be interpreted as YYYY-DD-MM. So that is an zero argument.
I never said that the date format should never used, just that significants is a arbitrary value, what significant means depends on the context. If YYYY-MM-DD would be so great in everyday use then more or even most people would use it, because people, in general, tend to do things that make their life easier.
There is no superior date format, there are just date format that are better for specific use cases.
My team switched to using YYYY-MM-DD in all
our inner communication and documents
That is great for your team, but I don't think that your team has a size large enough to have any kind of statistically relevance at all. So it is a great example for a specific use case but not an argument for general use at all.