Personally I find it more handy to know day (of week) than date (of month), but I don't think I've every seen a watch that does day-only, usually either date-only or day-date.
replies(4):
I don't know about you, but for myself I find the days kind of blur together (especially (during-COVID, post-COVID) WFH).
I rarely need to know day-of-month.