Do you have a JavaScript workaround for CSS that isn’t fully supported yet? Make a fallback for it. Have a slideshow? Fallback. Animated background? Fallback. I’m going to assume you’ve gotten the idea now.
To put it bluntly, if any part of your site breaks when the JavaScript does, you have failed. And JavaScript does break. If things go really wrong, it can break for thousands of users at a time. The only reasonably foolproof site is one that remains functional even when JavaScript does not.
Let’s take it further: Your site should ideally be functional even if the CSS doesn’t load. Yes, it’s an old argument; but is it really any less valid for its age? The job of any good designer or developer is to make sure their client’s site is usable under the widest possible range of conditions.
So yeah… fallbacks. Learn to love them.