Here's another way of putting that: SpaceX has designed it so F9 and Starship payloads will be interchangeable. That's not quite the same thing. You can't just take an F9 payload and bolt it on top of an Ariane rocket.
> Starship is being designed with the intent that it will cannibalize all Falcon 9 launches eventually.
Sure but that's just going to take a long time, particularly if F9 is, say, sub-$15m per launch. There's a lot that still has to be done for Starship (eg the landing system, the crew component).