Conceptually, it needs to take in account the type of date it handles. The question to ask is “does it matter when in the week or a month a date is selected?” or similar.

Under these considerations, I can say that for a "well known" date, like a birthday, or an expiration date, where the context of the calendar doesn't matter, it's not needed, and probably undesirable. (Under these contexts I would use bare selects/inputs with one for each of YYYY/MM/DD.)

For an appointment, or a time span? Date pickers are useful. “Which days are mondays?” “I want to book from a monday to the friday the next week.” Raw controls won't provide the context to help the user.

I feel the ones you fight against are more than likely those where you already are aware of a precise moment, in the first scenario. The others are more likely to leave no impression if well done.

With that said: Always de-compose the date picker in their discrete parts that a user can use. Make the picker fill these.