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Great answer, but it unfortunately is taken seriously. The reason is because it is an "end of the road" hypothesis. It tells you all the weirdness is fundamental and no further thought is required. Just like good old Copenhagen. The unfalsifiability is a virtue here, it's a complete explanatin without the messy testing. Now stop thinking, shut up, and calculate.
To be clear, the reason Many Worlds hypothesis exists in the first place is because it's a possible solution to the calculations. It's not that someone just came up with an idea to get out of doing real work. It's just unfortunate when the universe puts multiple possible solutions out of reach of experimentation. But hey, there was a long time of history where virtually any belief about the composition of the moon was considered unfalsifiable.
The "solutions" are not out of reach. Just do the experiment more than once, like any statistical theory.
The moon thing: yes because it was hard to get to, not impossible in principle. If the moon was in a parallel universe your analogy wouldn't be irrelevant.
Why is that unfortunate? It's an extremely well justified theory.
I'm not sure why you say this? If anything, that's a description of Copenhagen, which MWI is a response to.