Textual apps will eventually support this and other OS integrations exposed by the browser. It's never going to look native, given the terminal origins. But it will be possible for them to play better with the OS. And when we add PWA support, they will have a more desktop look and feel.
SSH is an advantage when running in the terminal. In the browser the advantage is that you can deploy them where you couldn't run a web server. Think IOT, routers, lab equipment. Or just cloud servers, where you want a backend to work with the local file system.
Another advantage is development speed. Textual has a learning curve which is far less steep that a regular web stack. It allows non-web developers to build bespoke apps.
I also think that TUIs can be more attractive than GUIs in some scenarios. Not because they look better, but you can build UIs that are snappy and keyboard driven. TUIs are a more natural fit for that kind of interface.