And forget about the "One Epic Landing Page" concept, that falls into that micro niche funk that I mentioned earlier. I think you've been fed some misinformation here, a blog post can rank just as easily as a home page from some micro niche site. If you do it right, easier.
I've never had a static site but I would imagine you would monetize it just the same as a blog. Wordpress is just the only thing I know how to use, and the long list of plugins is a huge plus. And many are geared towards monetization.
When you say "blog," I think you're referring to the blog homepages that display a list of the latest posts. You don't have to do that. I use a static home page, that way Google always knows exactly what it's about and what it should rank for.