It would be awesome if Stack Overflow's weekly newsletter contained questions/answers from the set of tags I have chosen to follow, rather than receiving a newsletter that has content with languages that don't relate to my interest.
I agree this would be good, although I wouldn't want to lose the random news. Sometimes things I specifically don't follow on the site are still nice to read about in a newsletter, and often grabs my interest.
I think this is good for promoting content and possibly getting more users involved in areas they might not otherwise view.
So perhaps leave it as is, but with an addition of a new section "Your Favourite Tags" (rather than this be "instead of").