Many paywalls rely on client side JavaScript to work. My guess is that this has something to do with search engine indexing.
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.
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.)