Perhaps 'annoy' was too strong of a term. What I meant was the kind of emails that barely interest your users enough not to mark them as spam. Low quality bacn.
What I'm saying is that it's not the death of newsletters. This new feature is really useful and its negative impact on permission based marketing can be reduced by ensuring that the content you send out is really appealing to your users. Which is a win-win situation, because more appealing content usually leads to more conversions.
A high open rate may mean that your newsletter ends up in the high priority inbox for a decent percentage of your user-base, despite being a newsletter (unless Google automatically excludes newsletters).