Many worlds is not a logical consequence of the non-deterministic view of quantum mechanics. One of the reasons cited in favour of the MWI is that it is wholly deterministic. That is probability doesn't appear at all in it's framework. This is much more in keeping with previous physical theories (Newtonian mechanics and Maxwell's laws of electrodynamics for example) which were also wholly deterministic.

If you're interested other reasons the MWI is often considered "nice" is that it is: linear, local, causal, realist, entirely unitary and in some sense (this is often disputed) minimal. Other interpretations have to add mechanisms (for example wavefunction collapse) in a rather ad-hoc way in order to stop many worlds happening.