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.
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I ended up settling on no-date watches, as I find setting the date to be annoying, and it’s not something I need that often. When I do need it, I have my phone. I think I’d ultimately feel the same way about a day of the week complication.