Adding a shortcut to a website to the home screen is a nice convenience. Unfortunately, it doesn't add it as a search engine to your iPhone search, or to Safari. Even with a PWA (progressive web app), the App is just a wrapper on Safari. For a startup like us, it is probably the best option currently available, and we've tried to make it a good experience. But it does suffer the same drawbacks as a regular App as a browser replacement. If you swipe down from the home screen and type something into your iPhone's search bar, you're still using Google and Safari.