The argument for your desired functionality lacks logic and common sense...

The system has no way of knowing whether a visitor is an existing customer, or a new customer, when they click "checkout".

(As it is about to become illegal - in the EU - to set such cookies, using this method to remember a customer is no an option).

I do not know of any web shopper who has been "offended" when presented with both LOGIN and REGISTER invitations.

People are not stupid... they will know which one to select...