How to add date of submission when a webform is submitted

This is correct. Default values defined on the column level in the base editor are not applied when a form is submitted. You have default values in the form editor for this purpose.

If you want a submission date to be set, use the created date column (see @AkDk7) or use an automation to populate a regular date column. The event is “New record” and you must add a filter that applies only to records created by the submission of the form.