If the website's primary purpose is to present content to the world, then I'd strongly advise against such an approach. Not only will you lock out users who cannot or will not enable javascript (think audio browsers, people with really really old software, sub-smartphone mobile devices, etc.), you will also effectively hide all your content from search engines.
If, however, it's a web 2.0-ish thing that resembles an actual application more than a content-presenting web site, then programming it in javascript might be a viable solution - but again, you'll miss out on search engine hits and javascript-agnostic users.
Also, note that there is nothing stopping you from calling your api's from server-side presentation code (ASP.NET, PHP, JSP, whatever you fancy).