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.