As you note, there is so much going on in the world of the front end that I don't think it's possible (for a regular, normal human - if such a thing exists) to be able to specialise in both front and back end technologies and do both equally well. As chaotic as the front end world is these days, I do still think it's an exciting time.
There used to be a lot of emphasis on how the stateless nature of HTTP put certain special considerations in your path when developing an online client/server application, but the proliferation of these front end frameworks is changing that.
RoR brought us a paradigm shift (and Cake, CodeIgniter et al) away from web sites with pages to the creation of applications with business logic and presentation layers. The frontend js frameworks are doing it again, in large part thanks to the likes of the DOM, Ajax and web sockets, thereby making it possible to deliver a fully specc'd client application to run in the browser, which in turn lets the back end be the business logic and storage - the server end of the deal.
If this is the case, then there's a future where a PHP developer can become an awesome PHP developer without even needing to know html, css and js. The line stops at providing an api that can consume and emit JSON.
These are all just my impressions on the matter of course, but I think there's a direct parallel in play here.
If "Full Stack" means doing a good job of both front and back ends, then I think there's also a natural ceiling that ends somewhere in the MVC-like framework realm. Beyond that, I think we're looking for specialists in either front- or backend. There's a point where "Jack of all trades, master of none" comes into play simply because of the complexities involved in each domain.
So no, I wouldn't consider myself full stack either. Trying to keep up with the chaotic world that is front end is more than a full time job these days. I can totally relate to Phil Sturgeon's tweet!