As a test, I whitelisted JavaScript in NoScript for theatlantic.com and the paywall appeared. I revoked it and it disappeared again. It appears to be purely client-side, not reliant on cookies or anything.
So my conclusion is that an archive indeed shouldn't be necessary; people can just disable JavaScript. It doesn't cause issues with the page formatting or anything.
Most browsers do NOT offer per-site JS disable buttons.
It should not be necessary to change the browser to view a website; people can just use archive.today, which works fine in all browsers with JavaScript, and doesn't require a captcha, either, in browsers that don't block stuff. (It only requires captchas in those browsers that do block stuff.)
So my conclusion is that an archive indeed shouldn't be necessary; people can just disable JavaScript. It doesn't cause issues with the page formatting or anything.