Caution: This post includes animated GIFs. Some people find these annoying (especially when, like here, they're not even funny).
There are plenty of good reasons to prototype your designs in HTML. (I posted a roundup a while back. And this post by Leisa Reichelt puts it even better.) But one of the most compelling reasons is that there are things that you can do in a prototype that you simply cannot do in any static deliverable.
Here are a few examples.
An animated transition to show that something has been removed makes the change less jarring and makes it more obvious what just happened.
Drag and Drop
jQuery makes it extremely easy to turn a simple list of items into a list of draggable items.
Yeah, yeah, I know—the only people who do this to their browser windows are designers. But the point is, if you build your prototype using a framework like Foundation (other front-end frameworks are available), not only can you lay out your page very easily, that page is automatically responsive—it works on any screen size. (Though it's up to you to make that work in a way that makes sense for users—just letting the content get reflowed doesn't always cut it.)
These are just a few examples of things you can do in an HTML prototype that simply can't be done in a wireframe or Photoshop comp. (There are many more.) Which means things that must be documented to supplement the wireframes/comps. Which means things that are open to interpretation. And to mis-interpretation. If you're not already prototyping in HTML, you should be thinking about it.