According to quantum mechanics, if a simple quantum mechanical system interacts with a complex one, the complex one is thrown into a superposition of states that can have no meaningful interaction from then on.

Many worlds says that quantum mechanics is all that there is, and all observed consequences can be predicted from the assumption that we, ourselves, are complex quantum mechanical systems. The prediction is that we coexist with superpositions of ourselves doing different things and cannot meaningfully interact with them. This seems weird to us, but is exactly what the theory predicts.

Consider Schroedinger's cat. We ask whether the cat is both alive and dead before we open the box. This puzzles us because that is what quantum mechanics predicts and that seems weird. Multiple worlds says that quantum mechanics holds, it remains both alive and dead AFTER we open the box, and while it seems weird, there is no actual contradiction anywhere.

So mathematically simple. Weird consequences. In perfect accord with our best theories and best experiments.

By contrast the Copenhagen interpretation says that there is a collapse somewhere even though there is no experimental evidence for it, and we have no theory about how it might happen. And the pilot-wave interpretation says that our best theories notwithstanding, the universe is something different and weird in a different way.

In any interpretation, it seems the same question remains:

Copenhagen: Why did the wave collapse into state A and not B,C,...

MSI: Why am "I" in multiverse branch A, and not B,C,...? (and who am "I" anyway?)

Pilot wave: Why is the pseudo-random seed = A', which I can only see indirectly by observing experiment result state A?

Brilliant - this is perhaps one of the clearest explanations of the disagreement between each of these interpretations I've seen, and it makes crystal clear why we can't hope to observe any differences: the questions are all fundamentally "why" questions, which we can almost never make direct observations to resolve.

At the root, we're always asking why some random variable ended up in a certain state. Our "interpretation" just changes where we ram that annoying random variable into our theory, which largely depends on where we're most philosophically comfortable with uncertainty showing up.

You are in A wondering why you are in A. You are also in B wondering why you are in B, and so on. It's all perfectly consistent.

I am in A, though. Maybe another me is in B, but why is this me in A?

'this me' in your sentence just refers to the one that is in A. Thus you seem to be asking "why is the version of me, that is in A, in A?". It just is by the definition of the object ('this me') your asking about.