Saved Addresses for WooCommerce

We sometimes (as an admin) create a customer account without placing in order. In those cases, we want to add an address from the backend so the user can start using his account with an address already available. However, when we add an address to the user from the backend (shipping and invoice), that address doesn’t show up on the My Account page. Ideally, an address that is added in the backend in the user profile is also available on the My Account page so the customer can manage and use that address.

Furthermore, an address removed from the My Account page still shows up on the checkout page. We would like to see a removed address is also removed from the list on the Checkout page.