Why static HTML?
Static websites were the only option in the past. Web Developers would hand code each HTML file of their website. This was a time consuming process causing a lot of re-work and was very error prone.
Static website generators have simplified the process of creating static HTML website by using advanced technology to parse the input files and spit out a full static website.
Below is an example input of a squido website structure where posts are written in Markdown and one simple command outputs a full static website ready for hosting.
Benefits of a static website
Static websites are dead simple. No learning curve of complex databases, frameworks, programming language, hosting tools and more. With simplicity comes more rapid development and reduced potential where things can go wrong.
Speed kills. Google loves a fast website and users do too. Google created AMP with the sole purpose of speeding up the web. There are differing opinions about whether AMP is any good but the idea of speeding up the web is sound and a great initiative. Static websites don't require complex a Web server, database, server side processing and can easily lean on the benefits of CDN hosting.
Without all the complex parts of a dynamic website, static websites are simply inherently more secure. Hackers cannot compromise databases and steal data, change content etc. Static websites are simply HTML and CSS and not much can go wrong.
You can host static websites anywhere these days. There are providers which now specialize in this type of hosting by caching, integrating build/generator tools, free SSL and much much more. Some hosting providers are:
Dedicated static website hosts generally offer CDN services which is basically hosting content in many geographical locations and servicing that content to the user using the closest destination. This allows for less network hops and generally faster serving of content. CDN providers also offer caching, proxying and many other complex processing to speed up the serving of content.