Perhaps not great for production since Wordpress automatically updates itself, and you would have to keep up with any changes. And not just for wordpress, but for any other plugins that use the database.
Edit: A single file fork (albeit 5k lines of PHP) of the plugin that looks interesting: https://github.com/aaemnnosttv/wp-sqlite-db
Most these sites are running a homepage, an about page, a contact page, and maybe one or two misc pages. They might have a blog that has two blog posts on it from nine years ago. But that is really it. MySQL is really overkill considering the scenario. SQLite's big "limitation" is non-concurrent writes. But this is rarely a problem with most Wordpress sites because they are single-author and they aren't updated very often. SQLite can handle plenty of reads to support even heavily trafficked websites.
Not to mention, SQLite's greatest advantage is portability. A single file contains your entire database. A non-technical user could transfer hosts or backup their data by copying their database file like it was a photo or an excel document. That's pretty incredible when you think about it.
I was a casual developer (i.e. not for work, just for personal) deep into the PicoCMS ecosystem for a couple years, a few years ago. I both started a site and helped a family convert an old static site to PicoCMS and really had no complaints. Re: frontend for the owner, I started with Pico Admin and made a bunch of modifications to it (including an image uploader) and the non-tech owner has no complaints and it's been working well since.
Nowadays for my own blog I'm into the whole SSG/JAM trend, but I'd still run a PicoCMS site any time, if the use case is right.
I've always been surprised WordPress didn't go with SQLite though - it'd have made deployment so much easier for 99% of users running a small, simple blog.