This trend, hosting blogs on static html, is kind of ironic, given how popular it is among developers. I can't make up my mind whether it's some sort of hipsterish-nostalgic thing, a general distrust of running other people's dynamic blog code, or just plain Occam's razor (stick to barebones).
On of the main reasons I like static site generators so much is that it makes maintaining a website more like developing software. I have 'sources', which I keep in a Git repo for powerful versioning, I 'build' the website from the sources, and then I 'publish' the final product... which is the user facing HTML website.
Developers just find that workflow sublime, and since we're often making websites for ourselves or for our companies, it only makes sense that we've started to use tools that fit our mentality.
I think this is a huge reason for the popularity of static blogs. For dynamic blog software, your choice is basically WordPress. Unfortunately, WordPress has a pretty bad security track record. Things might be different if there were a reliable second-place blogging engine, but as far as I know there isn't.
Another reason is the rise of version control for small projects, and the way static sites fit nicely into a Git workflow.
There is nothing "hipster" about it, it's a perfectly valid technical decision for someone who doesn't want to fuss with a janky, complicated WordPress installation or writing raw markup for each blog post or writing their own CMS. Frees up more time for developing things which are of any actual interest.
It makes getting good, scalable performance basically trivial. Static content distributed across CDNs means someone else solves that problem for you at low cost. Forget SQL injections and usually forget XSS. If you need a comments section, you realistically need outside help to filter out spam anyway, might as well use something like Disqus. Also, very few moving parts to break after deploy.
A static site on s3 or similar is essentially infinitely scalable: you never have to worry about whether it can stand up to some publicity and its performance will always be snappy no matter what. It's cheap. It's controlled in source control and backed up. Achieving those same things using other configurations instead of static files takes an order of magnitude more work and complexity.
Until you write a post that ends up on the front page of HN and it brings your server down. The chances of that happening are small, so it's probably not worth optimizing a dynamic site for that use case, but with a static site you don't have to do any additional work or introduce complexity.
I was developing a (java|coffee)script-only full text search engine (not just some simple regex match, but something memory efficient with succinct data structures) to have an answer for search, but than it occurred to me that I rarely, and in general never, use search on someone else's blog.
I am not a developer and I don't grow my own food or use typewriters (much).
My small vanity site has an update once a month or so. I use Linux at home. I hacked a few bash scripts to get a basic flow going...
* edit text file with markdown (vim or gedit). Save to a directory in dropbox that has images and files under it
* run a script that runs markdown and adds a header and footer
* run a script that adds the new page to an index
* run a script that invokes lftp that uploads the changed files to server space
I find this quicker than maintaining a WordPress installation. YMMV
What I do find amusing is the range of really heavy duty technology that some of the static Web site generators are using.
It appears to me that your workflow is missing several pieces. You are missing RSS, which will keep some people from following what you write on your website. You are missing a sitemap.xml file, which search engines care about. You could add support for these to your work flow, but they are pieces that require very little work to enable support for in wordpress (RSS is just there, and sitemap just requires enabling the add-on), and I presume are trivial to enable in some of the static generators like jekyll or hyde.