Honest question: How large is the noscript population? If I were to chose where to invest my time, catering to the noscript crowd would probably come pretty low on my list of priorities.
Very often websites that don't work without JavaScript have serious design/privacy issues, which better be fixed even if no one disabled scripts. Very often the reason those websites require scripts is because the developers working on them are incapable to conceptualize desired business logic using some simple mental model, so they just throw random code and libraries at the issue until it seems solved.
Saying that "it's an app" is a common, but very weak excuse. Most websites are not doing anything that would warrant them an app status. They simply use JavaScript to enhance browsing experience. That's perfectly fine, but the inability to isolate those enhancements from code logic that's required to make the website work is indicative of the problem that I described above.
I'm not sure I understand your logic here. Many sites use javascript for advanced features not possible otherwise. I don't see how not working without javascript equates to privacy issues.
Stuff like including Google's JavaScript by linking to Google's servers equates to privacy issues. The fact that some websites don't work (at all, don't even render) without external scripts is a design issue. These issues often come hand-in-hand, but no one said that one equates to the other.
Also, if your notion of "advanced features" includes rendering of text and images and working links, you might consider re-thinking it.
I wouldn't want to browse with anything but NoScript, CS Lite, RefControl, Adblock Plus and Ghostery. If your site doesn't work, too bad for you. I'm not the person who makes a living selling stuff on the interwebs.
The "Gawker Experience" (white page, nothing of value is lost) is quite common, and I like it.
There are useful applications of Javascript, but they are rare. You have to show me that it's useful to me, and I will then give you my CPU time. Not the other way round.
I guess the only way to know how relevant it is to cater to noscript users is to measure how large a chunk of potential customers your leaving behind relative to the cost of fixing your site to work without JS.
Bingo. Since I first installed NoScript, I've started noticing a correlation between how gracefully your mostly-static website degrades without javascript and how worthwhile your content is. Those that fail completely rarely have anything worth looking at on them anyway.
If I understand it correctly, OP was redirected to a dumb-down instruction page of how to enable Javascript in his browser. What he actually wants is the reason "why" he must enable Javascript for the site.
You can win over noscript population very easily by taking a little bit of time and explaining your app with some amazing screenshots.
My prejudiced view is that it's such a small part of the population it's not worth caring about, though I'd be glad to be proven wrong.
If doing pages that require javascript to even run in the first place is a good idea, I think is a different discussion.
<noscript>To enjoy all this awesomesauce, please enable javascript:
<img src="/annotated_representative_screenshot_you_should_already_have_for_the_tutorial_page.png" />
</noscript>
It also depends greatly on the kind of web app you are making. If your audience is highly tech-savvy then caring about noscript population will increase your userbase.