The biggest cons of it are that you must rely on the end user's client browser to correctly render all of your content. An out of date browser or an untested browser is likely to result in broken content or no content. This is distinct from and more severe than the problems those same browsers encounter with HTML & CSS they cannot correctly render. If the markup is supplied to the browser, it may incorrectly render the CSS, but at least the content will be accessible. Using a script to generate all the markup can easily result in no markup being generated.
Then there are the users who run without JavaScript, or with something like NoScript blocking most scripts. They'll not see any of your content either. Thirdly, your content will not be indexed by most search engines.
Addendum
Relating to developer skill sets, working strictly from a JavaScript framework could tromp on the web development division of labor somewhat, if you have such a division. Unless the framework is able to maintain a good separation between the generation of markup, CSS, & application script, your programmers may find themselves more deeply in the role of designer and content editor than they are accustomed to (if you have a division of labor between those aspects of development).
From the comments below, we learn that this is intended for an intranet application in a controlled browser environment. This moots the end-user testing issues mentioned above to some degree, but there is always a danger of a browser upgrade breaking application code in JavaScript.
I cannot think of any positive outcomes that would outweight the potential negative outcomes (by my own judgement, anyway)