"Dear user, change your browsing habits to save us a few hours of work"
In my opinion with the multitude of great new JS libraries (particularly knockout, backbone etc) and JS browser features we're going past it being as simple as progressively enhancing your site. If you are a startup trying to do things in a lean fashion it must be hard to justify.
This is highly dependent on a number of factors, mostly:
* The kind of site we're talking about, if this is a real-time chat application it makes sense that it can't work without JS, if this is a company site or a presentation site for an appstore application with an embedded video and you can't make it work without JS you don't know what you're doing.
* Whether this was considered from the beginning or whoever built the site just went wild with javascript without consideration.
And even in the first section of the first case, if the unlogged account-less front page can't work without javascript I'll probably still think you don't know what you're doing.