Hi,
If you're using PayPal, you should be able to get the information of the users via PayPal.
For other payment means, you indeed won't get any information if you removed both the "login" and "address" views from the checkout.
I would indeed recommend to keep the "login" view. Instead, you can change the "registration" option of the Checkout tab of the configuration in order to only ask the email address and the address of the user. Then, regarding the address, you can customize the address fields via the menu Display->Custom fields.
So if you want it to be simple, you could have only the email address field.