The problem being, the date picker is already a (single) input field. Having multiple input fields for what is already an input field somewhat defeats the purpose.
This doesn't address the real problem, though, which is IMHO that a calendar-like presentation doesn't lend itself easily to numeric date input/selection, especially, if it's about a date outside the current month. (E.g., a 3-column list view, which could be operated both by mouse/touch and keyboard input, may serve the purpose a bit better. Safari mobile could even style them rolodex-like… Which is, BTW, how it used to work on Safari mobile, before they switched to the unified style.)
This doesn't address the real problem, though, which is IMHO that a calendar-like presentation doesn't lend itself easily to numeric date input/selection, especially, if it's about a date outside the current month. (E.g., a 3-column list view, which could be operated both by mouse/touch and keyboard input, may serve the purpose a bit better. Safari mobile could even style them rolodex-like… Which is, BTW, how it used to work on Safari mobile, before they switched to the unified style.)