Well, advertisers may disagree: Twitter showed ads to non-logged users too. And I don't have any figures of the logged-in/logged-out views, but if they are somewhat near Tumblr's, they are just losing A LOT of ad views.
And, ultimately, it's not users who will kill Twitter: it's advertisers. The moment all the big spenders decide to not pay for Twitter ads anymore, Twitter (as a company), will be done.