For single-user single-device scenarios, that's totally doable. It's called a purely-local app.

Where it gets complicated is there's a (totally understandable) expectation these days that your data is synced across multiple devices, and you can collaborate with other users, who may also have multiple devices themselves. In practice, that necessitates some kind of always-on server that maintains state for everyone. A phone can technically do that, but you'd probably kill your battery in the process.