The main issue with this line of argument is that you don't see people who like other interpretations claiming quantum computers won't work. Saying quantum computers imply many worlds is the classic mistake of wanting to show A=>B and arguing B=>A instead of ~B=>~A. If quantum computers were inconsistent with collapse interpretations, you'd expect people who think collapse interpretations are correct to be confidently predicting quantum computers will never work. But they don't; they just think the state inside the computer isn't collapsing.

I'm often tempted to argue quantum computers at least clearly favor ontic interpretations (ones where quantum states are real). Because good luck computing things by subjectively having a computer instead of actually having a computer. But, as far as I know, you don't see quantum-bayesianism-ists having any qualms with quantum computers. I think because if you're already biting the bullet of interpreting diagonally polarized light as subjective, and Bell tests as subjective, then interpreting a computation as subjective isn't fundamentally different. It's just more in your face about it.