It's not just web pages that benefit from proper web-style sub-headlines. As far as I'm concerned, proper means sub-headlines of 4-10 words that summarise the next chunk of information. They improve practically any business document.
I have just read two short editorial reviews of some web content. Both are supposedly written as friendly letters, supposedly structured for the benefit of the client - a branch of the Cats Protection League.
One has web-style sub-headlines, so that the client instantly gets the gist of all the main points:
Home page: a fresh, fast hub
Adoption: simple, clear and logical
Bequests: just three steps!
Formatting and punctuation: minor changes
The other review sticks doggedly to old-style generic headings, so that skim-reading tells the client nothing. These labels merely indicate where a certain type of information is located. Spare me.