Some tasks (like a daily review) can’t be begun until the day they are due. Currently the UI for Asana though, only allows a start date to be entered if it is not the same as the due date. If you try to enter a start date which matches the due date, the start date is silently discarded.
Allowing a start date to be set which is the same as the due date would allow a more realistic view of tasks and facilitate tickets like Ability to Sort tasks by start date - #9 by Daniel_Raymond, Allow for Due date = Start Date + NUMBER, and Support hiding tasks where the start date has not passed
A previous request for this same feature was merged into a ticket which was only tangentially related and then closed.