I agree the original quote doesn’t present a very strong argument against the MWI. In the same way that arguments against determinism in classical physics are not very convincing. But seemed worth pointing out.
In the MWI case it’s not clear how sensitive the “worlds” are to the in initial state. It’s not even clear how sensitive they are to the current state! Better understanding of how (and how many) worlds “emerge” would be needed to say if the “problem” is or not as bad as in the classical case.
Is the number of worlds stable? Is it increasing? In any case, those worlds are the inevitable consequence of the initial conditions even though we can’t even estimate how much fine-tuning is needed. I don’t think “randomness generated along the way” is a satisfactory counter-argument.