The problem is that QM doesn't allow randomness at the fundamental level. The Schrodinger equation is a linear differential equation, systems that evolve according to it evolve just like classical mechanics.
However, when you measure the state of such a system after however many steps of perfectly deterministic interactions you want, you find the system takes only one of the many possible states predicted by the Schrodinger equation, with a probability that depends on the amplitude of that state.
It is this discrepancy between the deterministic nature of the quantum world and the classical world, but the probabilistic nature of the crossing between them, that people find disconcerting.
MWI even does away with this to solve extent, explaining it as a kind of observation bias: as a particle interacts with a very independent system, it loses its ability to interact with itself (decoherence), and so we get many versions of the system each interacting with a single version of the particle, which stimulates classical physics for each version. From the perspective of any particular version of this system it is random with which particular version of the particle it interacts, even though at the universal level there is no randomness.
what if randomness is an inherent property of nature?