> I can set the default browser on my iPhone to Chrome, right in the Safari settings.
You can set your browser to a Chrome UI wrapper around a Safari Webview. You can do this with any [browser] UI wrapper around a Safari Webview, as long as [browser] has received the relevant entitlement from Apple.[0]
Outside of the EU, all browser apps on iOS must run Safari's engine.[1]
[0]: https://developer.apple.com/documentation/Xcode/preparing-yo...
> Request the default browser entitlement by filling out the Default browser entitlement request form. If your request is accepted you get both the default browser entitlement, and the com.apple.developer.browser.app-installation entitlement. If you have the default browser entitlement, fill out this form to receive the app-installation entitlement for your browser app.
[1]: https://developer.apple.com/documentation/browserenginekit
> Important: To distribute an app that uses an alternative browser engine, you need to request the relevant entitlements for your developer account. For more information and to request the entitlements, see Using alternative browser engines in the European Union.