I wrote my blog's static site generator 10 years ago and I'm still using it. If I want something it doesn't do, I change it. It's still a single-file perl script and it's easier (for me) than any other option.
You talk about mobile devices but it seems obvious that I would never want my phone to constantly serve content online. Not only it would saturate my mobile plan but would drain my battery life and grind the device to a halt. Same thing would be true for laptops, which could not even function outside wifi or cable range.
The is actually one single device that could serve this role: the smart home manager. Be it a homepod or a nest hub. It's basically the only powerful and well connected device people have on 24/7 in their houses. But then again, what about NAT and dynamic IPs?
People used to do this in the 90s and early 2000s, but it turned out to be a hilariously bad idea security-wise. Even the enthusiasts these days use a dedicated server somewhere in a datacenter. Services like Github Pages and Cloudflare exist for a reason, and it isn't because anyone is trying to gatekeep web hosting.
I love having a completely independent working local copy. My environment is perfect for my needs or I change it.
Basically my deployment plans and disaster recovery are indistinguishable.
There is no custom executable to run, there is no need for authentication, there is no need to write files to disk, there is no need to parse user-provided content, there is no need to access a database, there are no custom libraries to update... A static website can literally be "upload and forget", and that simply isn't the case for dynamic sites.
You get everything anyway, and nothing you do is used by the server.
Of course the server itself can be attacked, though it is much more difficult then with dynamic sites.
Part of why I use static HTML on GitHub pages is it’s easier and cheaper than dealing with the complex toolchain needed to self-host something like WordPress or Ghost.
I’m skeptical cheap and easy is something inherent with static sites.