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.