Let me use something besides awful cloudfront and I would so do this.

As it is, I just run it in my amazon VPS that I have for other things anyway.

I'm from Netlify. The point of the platform is that it's like 9 services in one. With free SSL that is renewed automatically and free hosting of Custom Domains. It also provides a specialized CDN that does Instant Cache Invalidation even while highly cached, atomic deploys, Continuous Delivery, Prerendering, Formhandling, and so much more. Perhaps you are thinking of static sites being merely tiny sites that have little or no updating, and doesn't need much of a workflow around it, and offers few features. There are solutions that's great for a small personal blog or a prototype. But if you are looking to do commercial sites, from smaller sites, to large enterprise sites with hundreds of contributors, multiple languages, and tens of thousands of HTML pages, then a viable and performant workflow is needed. This is what Netlify does. Integrates and automates all the services that goes in to deploying and maintaining a commercial-grade modern static site.