First, "Vary:Accept" and Vary:User-Agent effectively nullifies shared caches. Because instead of saving 1 copy of a response for a URL, and serving it to all requests, a shared cache has to save 1 copy per unique combination of URL and the Accept request header and/or the User-Agent header sent by the browser.
Browsers send wildly different Accept header values, not only across browser vendors but across versions as well. And the User-Agent string has insane variation since OS, CPU, language, and more can be included.
The net result is that all these unique request header values fragment the shared cache so much that you don't get any cache hits. The shared cache has been nullified.
Second, if the HTML is a static file, yes you have the same problem. However, in the modern age of web publishing, the HTML is almost always being dynamically generated by some application logic/CMS/something. This means that it is rarely is ever cached or marked as cachable to shared caches.
More about Vary and shared caching: http://zoompf.com/blog/2010/03/the-big-performance-improveme...
http://blogs.msdn.com/b/ieinternals/archive/2009/06/17/vary-...
Unfortunately, “done properly” excludes things like nginx's cache module, a number of CDNs, and even certain browser caches. Some of the bugs are obvious – e.g. returning gzipped data to a client which didn't request it – but others will simply require monitoring to realize that your cache isn't caching anything or has a dismal cache hit rate because every permutation of request headers and the values referenced in Vary are being treated independently. Worse, all of these can change unexpectedly due to updates in “stable” software so you need deep monitoring checks to ensure that everything is still working the way it was when you set it up.
The more I've used content negotiation, the less I'm convinced that it's a desirable feature. Unless you tightly control the client, server and all intermediaries you'll spend a ton of time on operational overhead and the alternative is that you simply use unique URLs which will always work correctly after the initial implementation, which is also easier.
Also, if you respond with different HTML, you still get the caching issue, because you may mistakenly serve cached HTML linking to WebP images to non-capable client. So the cache should still consider Vary and Pragma headers (or it's broken).
The only thing I don't really fancy about "/cute/kitten.jpg" serving a WebP image is ".jpg" part. If content-type may vary, the "extension" part of the "filename" should be generic ("/cute/kitten.image") or missing ("/cute/kitten"). That's for saving pics, when URLs transform into filenames.