The problem is a web browser is arguably something which has a webview in it. The difference Google considers between "a browser" and "an app embedding a webview" is whether that app is specifically Chrome, Firefox, Edge, Safari, or IE.
How up to date the embedded web engine is (and how quickly you would be able to merge upstream changes, update the framework, wait for "browsers" implemented using the embedded framework to update their dependencies, etc.) That can be a pretty big deal when there's a fix for a high-impact vulnerability.
With a known browser, you get reasonable guarantees that TLS is being handled properly. With an unknown browser, these guarantees are gone. Considering the average person has no idea what https/TLS is, banning all unknown browsers as a defense against phishing seems completely reasonable.
For the most part, if a browser's extension store isn't in order, everything else they claim to do to secure web traffic is kinda a joke.