The 10-day deadline was set for withdrawing a person's consent with regard to an activity mentioned in clauses 7, 8 or 9. The process by which a person's consent is withdrawn is often automated. It could be someone requesting that their name be removed from a marketing list, which is normally done through an automated process.
A deadline of 10 business days gives enough time to small and medium sized businesses that traditionally do all this manually. For example, the business might make the change to their list manually and finish the work later. Ten business days equals a minimum of two weeks—maybe longer if we consider the Christmas holidays. That is enough time.
The text clearly says without delay and no later than 10 business days.