Sure, but they need to be generated by some sort of framework, somewhere. If your definition of a static site includes framework-generated index pages and page structures, aren't almost all websites static already? Making them tiny is just a matter of writing better templates, not picking more obscure frameworks.
In my books the difference lies in how the HTML is generated. In case of static sites you generate it only when you rebuild the site after changes. In dynamic sites you build it dynamically on each request. Sure, you can cache the hell out of it and have a feeling that it's the same, but the truth stays that perhaps you're doing 50 SQL queries for a simple "welcome on our site" landing (something I actually witnessed some years ago). And with caching you're achieving the result with adding another infrastructure layer on something that could have been dead-simple from day one.