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Here’s an interesting example:
The Bell test about entanglement is one of the best-known proofs that quantum mechanics can’t be explained using classical statistics.
The Bell test is an analysis of the correlation between two entangled particles.
However, that correlation is only notable because we are analyzing the evolution of both particles.
If we analyze one particle, alone, we wouldn’t be able to determine if it is entangled with any other particles (and we wouldn’t be able to model it without the need for quantum mechanics).
In other words, you only need the “other worlds” when you are analyzing a system and trying to predict its behavior. You can completely ignore all information or “other worlds” external to the system you are studying.
That seems to demonstrate the opposite of your argument though, because the other particle does still exist even if you don't consider it.