Why is it faster for my delivery if I give authority to leave by entering a location for the courier to leave my goods into the checkout?

When your courier sorts his deliveries for the day, usually thye will prioritise all authority to leave parcels to be delivered first.  The reason this happens is because they know they will receive their delivery commission if they go to your delivery location.  If they need a signature, they aren't sure and will probably leave your item until all the 'easy' ones are delivered first.