It does depend on what the site is trying to do, but for the most part on the majority of websites -- YES! Why? BECAUSE THAT'S THE POINT OF HTML IN THE FIRST PLACE!!! Device independance (sometimes called device neutrality) is the entire reason to use HTML to deliver content. We got away from that during the browser wars and many developers never returned from that dark evil place, but that's what strict, separation of presentation from content, and progressive enhancement is all about.
It's why the best (IMHO) approach -- even if you're handed a goofy picture by a PSD jockey -- remains coding semantic markup first (pretending the pretty picture/layout doesn't even EXIST), creating the layout with CSS, going into the paint program to make the images (or slice out of the original PSD if working from that) and hang them on the layout using CSS, and finally to add scripting behaviors to improve the user experience, avoiding ones that just suck on bandwidth like candy and provide no REAL enhancements to functionlality.
You work that way, and it's no harder to have things work as the "gee ain't it neat" technologies vanish. Progressive enhancement means graceful degradation. Failing to provide that, particularly if the content is just fixed text and objects, misses the point of HTML, the point of the Internet, and amounts more to ignorance and ineptitude than skill.
When it comes to JS, I don't think I've ever turned it off, and I've never hit any sort of exploit, or any page that produces some sort of visual horror. Perhaps I should start visiting porn sites?
While I repeatedly come across websites with broken/buggy scripts, scripts that are just outright annoying with the animated crap that breaks even simple things like forward/back, opening in new tabs, or directly linking to a section of content... and we're not talking porn sites here... Lands sake I'm becoming increasingly concerned over how it seems like the porn industry is more reputable than most of the fly-by-night sleazeball scam artists out there developing sites for people.
There will always be less capable devices -- every blasted year for the past DECADE we've heard "oh nobody uses that resolution anymore", or "nobody turns that off" -- then some new device - like a netbook, or a smartphone, or a pad -- comes along and is a pimp-slap to everyone who said that. Same goes for the "oh bandwidth keeps increasing" which gets a backhanded slap with people browsing on bandwidth throttled or metered 3g connects, pay as you go metered caps on home connections (which I'm sure all our Canadian, Kiwi and Austrailian friends would be MORE than happy to explain to you) or entire counties in the US where 33.6 dialup is STILL a good day... Like Coos County NH, most of western ME, the Dakota's... Those are the people who turn things off, resort to things like Opera turbo (one of the big selling points for Opera mini) and in general aren't even going to bother repeat visiting any website that sucks down half a megabyte in scripting ALONE to deliver 2k of plaintext and five static content images. Say hello to Mr. Bounce Rate!
If there's anything I've learned over time is that the scale expands BOTH directions, not just up. Just because you're sitting at home with a 32" 2560x1440 Apple Cinemadisplay doesn't mean the guy on the HTC One is going to have the same experience on a website. Again, see why "what you see" should never be expected to be "what the user gets" when it comes to the internet. (and why WYSIWYG is a steaming pile of /FAIL/ alongside px for content fonts and fixed width layouts)
... and it really boils down to practices that should be done from the START of working on a site, require no more effort -- and as such failing to practice the entire REASON that HTML and CSS exist boils down to what Eisenhower once called "an apathy that had its roots in comfort, blindness and wishful thinking."[/ot]