Works over SSH, low requirements, and cross platform are some good reasons.
Ultimately though, I would like Textual to simply be the easiest way of creating a useful UI. Something that you could quickly become productive in with just Python skills. There are a lot of new Python developers that didn't come from a web background, but still need a custom UI.
I don't see it as replacing web apps. If you have the skills and you think you need a web app, then you probably should make a web app. I see it more as allowing UIs to be built that simply weren't being built before due to a lack of skills or resources.
This may become moot, because we have plans for the same API to also serve web applications.