The reason for this is that if we take the most improbable outcome of a given wave function and say “This highly improbable branch occurs once”, we are immediately contradicted, as the next least improbable event is virtually certainly a non-integer ratio to the former. So, we give the wave function numerical factoring / self-resolving capabilities and instead, the least and second least improbable branches occur the number of times necessary to maintain status as whole integers with correct relative ratio. But then, that only resolves two possible events on the wave function, and so with the third least improbable event, almost certainly not an integer ratio to the first or the second, we must repeat this step again of multiplying the number of branches for the least and second least improbable, to maintain a consistent integer ratio for our types of branches. As you can see, as you follow this up through all the possible branch outcomes, to express their corresponding probabilities in whole integers counts of quantum outcomes, you essentially have to engage in a massive computation of finding common factors all the way up. Further, even the least improbable event will require an incomprehensible number of duplicate branches, and the most probable events will have an even more innumerable count of duplicate branches still.
The only way I can see to escape this madness with MWI seems to be give up on the notion of truly separate branches, and instead treat these “many worlds” as a stream of overlapping world-ish-nesses in which discrete outcomes don’t actually even exist, but then you have seeming contradictions in observable discreteness and it’s not clear it’s truly even MWI anymore.
Disclosure: I’m not a physicist, and it's quite plausible that I don’t know what I’m talking about.
That's what it is. A measurement is coupling a quantum event to a statistically irreversible process. The total wave function that results has two major lobes. There's no split on measurement. That's why it's appealing: it makes no reference to classical mechanics in the formulation.