I know I've suffered this myself I don't think it's a sin "I often find I can't do things until I am logged in"
By default, when you register a post type, WordPress sets the value of the required capability for Add New to that used for Edit (i.e. All Posts). If you want to prevent users from using Add New content but still allow them to Edit content then you will need to assign different capability names.
But that’s not all. With the current version of WordPress ( 4.0 ) you need to implement a small workaround.