Websites differ in their basic nature, and one size does not fit all. Roughly speaking, websites that are document-like (primarily consumption-oriented) should probably be progressively enhanced; websites that are tool-like probably should not (interaction oriented, like gmail, analytics apps, other saas). Websites that fall in the middle will have to carefully consider the user experience benefits and the available technical/operational resources.

The upside is that progressive enhancement can refer to a spectrum of techniques. Deliver only above-the-fold content as HTML, inline your CSS/JS, inline the initial JSON data, omit <form> POST support, etc. Two templating systems do not need to be supported. It's a straightforward technical problem to apply JS templates server-side (and I'm speaking as a boring old .NET developer--Nustache and Edge.js come to mind).

Btw, another benefit of progressive enhancement can be SEO.