My claim is that almost nobody would jump to that interpretation because there is no pre-existing convention with year first and day and then month.

I guess if you'd never seen an ISO date before, and you were accustomed to DD-MM-YYYY, then it could still be ambiguous. It's all context dependent anyhow—who's to say 2023-07-13 is a date and not an arithmetic expression, or a code in some filing system that happens to look like a date.