There's no cert because there's no need for one in the first place. Mentioning that is pretty silly - it's obvious that there's nothing wrong with a static site with now cert, and no one is arguing against that.
Good to note. But I think you're distracting from the article's talking point.
I disagree with "switch to HTTPS or lose ranking", but that's an HTTP vs. HTTPS issue with Google's search ranking, not about Chromium or Mozilla. This article is about Chromium & Mozilla making stricter rules for HTTPS certificates. That's not a bad thing, to hold HTTPS sites to a better standard.
The whole "Let's Encrypt should solve all your problems" attitude is arrogant and short-sighted.
1) In my experience the user experience even for technical admins is still flakey on at least some popular platforms. In other words, it's not as incredible as you think.
2) It's not available to a host that doesn't connect to the internet but does occasionally get connected to by a local browser (eg. IoT firewalled inside my LAN is one obvious such case; I'm sure there are others).
And most importantly:
3) You'd have to be insane or naive to accept an architecture that leaves you dependant on a single vendor (especially if you need that vendor more than they need you!).
Me. I use shared hosting on a server that runs a reverse nginx proxy to my nginx server. I don't have root on the server. I have a LE cert that I need to manually fiddle with DNS settings every 3 months to get. If you know how to automate it I'd love to hear about it.
Why doesn't their nginx proxy /.well-known/ requests for your domain to your nginx? Then you could just use `certbot certonly --webroot --webroot-path /path/to/webroot/for/your/domain -d your.domain.name -d www.your.domain.name` once and put `certbot renew` and nginx reload in crontab weekly, and you're good to go.
If you can't use HTTP-01 and must use DNS-01 challenge, I would check whether the software that runs your host's DNS management panel has an API in addition to manual mode. If not, I would check for ability to automate HTTP requests to that tool (parse the HTML, submit the forms, basically). My hope would be that the tool is popular and someone already did the work and code exists to operate it as if it had an API.
If you can do that, you can write (or find one already written) a certbot plugin that performs the DNS challenge using your credentials to the host provided DNS settings. certbot has number of plugins for the big hosting providers: https://github.com/certbot/certbot
certbot is the most popular Let's Encrypt client, but it's not the only one. Maybe another client has support for your situation. I would maybe ask the support of your hosting provider, maybe they know something.
That's me! I'm technical enough to self-sign for ssl for my sites (it and tor are what I do instead) but I run on lots of old hardware and old (>5 years) OSes. The tools for constantly re-updating letsencrypt simply don't work and all the containerizations didn't exist yet. I've tried nearly a dozen LetsEncrypt updates solutions, compiled from source, from debs, "standalone" only bash solutions, etc, there's always a catch that prevents it from working.