This is not quite right though. In objective collapse theories, there is an "us" to do the observing, and there is a collapse event which samples randomly from

This is not quite right though. In objective collapse theories, there is an "us" to do the observing, and there is a collapse event which samples randomly from the possible outcomes. Both the "us" and the sampling are additional things that we have to add to the theory. In MWI, there is no "us" in an objective physical sense. "We" are on all the "branches" of the wavefunction, spread out in such a way that it isn't possible for any observation to see both events having happened. We don't "observe a random part of the universe", we do observe all parts of it. It's just that "we" aren't classical in the sense that you are implying.