With both " Enable registration on the “Checkout” page" and " Enable Guest Checkout" disabled checkout page when not logged in now shows only a simple message that user need to be logged in. That page is not affected by checkout template.
One workaround is to edit checkout page manually with bricks and conditionally display [woocommerce_checkout] (that will use template) when logged in and custom content like login form when logged out.
It would be nice to have either a separate template for that or build-in redirect to account page / displaying login template instead.