The comment I was replying to was wondering why people installed apps to read email instead of using the browser based clients. So I don't understand your point ...?
To be clear, a "Web UI" usually refers to a desktop or mobile application whose user-interface is built with web technology (HTML, CSS, JS etc.) that is rendered using a webview component in the application. You don't refer to a website (even if it is a web-based application like GMail) as "Web UI". It is still called a website. And while you are right that browsers today can store data for offline use, nobody considers it good enough for a backup.