If making such a change, why not make it even simpler: use year + day number in year. e.g. today is 2023 day 309 (or day 308 if more sensible 0-based indexing would be used)
And keep the named 7-day week cycle as-is independently of that, this one has been going for millenia and we need some weekends after all
And keep the named 7-day week cycle as-is independently of that, this one has been going for millenia and we need some weekends after all