This functionality is required according to customer perspective because it is not mandatory that user will checkout with his default address , what if user want to checkout with other address,in this case he need to go to his profile first and then change his default address.
You can take the reference from below attachment:
Also you can take the reference from amazon
This is required because no one want to fill address everytime for checkout. In magento also if user have checkout with any address then at next time of checkout that address will appear on checkout page, if user has use multiple address than all those address will appear on checkout page.
Please check the magento checkout functionality for this.Also please add an option on checkout page to add new address at time of checkout.