Combine the Login/Register for both WooCommerce and basic

For now you have a beautiful Login/Register widget which yet doesn't work in combination with the WooCommerce "My account". Yet in the WooCommerce Registration section (if it's not a checkout page) the users have only the Email field which sometimes is not enough. It would be great if you either add the "password" field into the Woo Registration section, or make some kind of the connection between the "Login/Register widget" and "My account". To be honest, I don't really understand why would anyone need the registration form on their website if it's not connected to the user's account. Thank you in advance.