It seems to me that one of the main reason why people use a calendar widget in a datepicker component is to see the days of the week when they are selecting a specific date. It also allows a user to provide input for three fields with one click (after they have narrowed down the selection). In terms of the amount of effort and ease of use, I think there isn't too much difference between clicking on three separate dropwdowns versus clicking on a calendar widget, other than the fact that you can see days of the week. In fact, it is probably easier to select the day field from a dropdown with the days listed in order rather than the inconsistent position of dates in a calendar.
Would it be easier for the user to just choose the day from a dropdown that shows the day of the week?