No, obviously not. If Apple were to allow third-party web rendering engines but disallow third-party web chrome that would be equally ridiculous. But just because one part of a browser is important doesn't mean that other parts of a browser aren't also important.
> And it has a rendering engine: the iOS WebKit engine. It’s not Google’s preferred rendering engine and Chrome isn’t my choice of browser well, anywhere at all actually, but it’s still a functional web browser.
It may be a functional web browser (honestly arguable given how old and buggy the iOS rendering engine is), but it's not "Google's wildly popular web browser".