I've logged this request in our project tracker as a request for a plugin system for post published event. This would enable plugging in custom code that fires when a blog post is published. Then maybe I would consider making an add on product to integrate the blog with the newsletter and trigger generation of an edition based on the blog post and sending it to the subscriber list. This way it could leverage the already existing newsletter subscribe/unsubscribe mechanisms and spam law compliance.
For now what I suggest is manually send a newsletter with links to recent blog posts weekly or monthly or whatever frequency you need.