> Being awake for longer requires larger batteries.
What if you remove the battery altogether and use the phone as an alternative to a Raspberry Pi, instead of creating more e-waste?
If Android (or any other mobile OS) wasn't so locked down, we'd definitely be able to take more advantage of devices like that and not just for hosting stuff - they already have mobile data support, Wi-Fi, Bluetooth, a microphone, camera, GPS, accelerometer and so on.
In regards to load, my blog did fine with one of the articles on the front page of HN way back, and it was served from a container that has about 1 CPU core given to it and under 1 GB of RAM (albeit it's still a rented VPS otherwise).
My homelab server CPUs have a TDP of 35W and I use those for CI as well with no issues. My netbook has a CPU with a TDP that's around 15W and it can serve web apps with no issues, alongside Visual Studio Code and a desktop environment.
A phone is almost certainly good enough for simple workloads as well, like serving static files or interacting with a SQLite database, assuming that your content wouldn't get too popular.
But having it be a server while in your pocket is probably too niche of a use case, rather than having it on a shelf somewhere, connected to a power cable.