I would bet the security claim holds up, I have definitely seem more RCE mentioned from Chrome than from Safari.

I would bet Google's track record would easily allow them to defend this in court. More an issue with Google though.

I guess that might have something to do with the fact that Chrome is vastly more popular than Safari, and also available on many more operating systems.

No, it's definitely about control. Allowing an arbitrary browser means allowing access to platform stuff from portable (gasp!) APIs. And Apple doesn't want that. They want an iOS app to be the primary face of everything important, and the other stuff to be an expensive port.

And the problem isn't abstract. Safari lacks a ton of very useful API implementations. Like, try programming a QMK keyboard on an iPhone: it's literally the only platform in the whole world unable to run the Via web app.