Because it drops straight out of the schroedinger equation, which is something you were already believing.
Do you consider believing in distant galaxies, rather than a novel type of astronomical object, to be more or less parsimonious? It means multiplying the size of the universe by millions; nevertheless most of us accept it.
Might as well quote Sean Carroll again, he's an expert and I am not:
"The Schrödinger equation tells us that there's a wave function that evolves over time and then you can ask how I can divide that wave function into a set of decohered non-interacting worlds and those are the worlds that happen. It is nowhere close to saying everything happens. It is what is predicted by the Schrödinger equation That is what happens."
https://www.preposterousuniverse.com/podcast/2024/05/06/ama-...
Interestingly, people seem less bothered by the idea that the universe might be infinite in size even though that has a similar feature that a lot of things happen. So it just seems to me that the discomfort is people worrying about the idea that there are copies of themselves out there somewhere when they really shouldn't. At least no more than if in an infinite universe there would also be infinite repetition and infinite identical "yous". This is starting to sound like a Douglas Adams bit now :D
Counting all daily QM-influenced events everybody experiences (a cosmic ray either passed through me or decayed before it reached me, a radon atom either decayed in the air right next to me or not when I went to my cellar etc.), I think it is fair to say there are nearly infinite copies of you in various multiverse branches (of course, some who collected lots of radioactive decay events are already dead from cancer by now).
Arguably this would be limited by the reporting accuracy of your equipment, but perhaps the thought experiment can be tweaked to get around that...
MWI has always suffered with issues around probability. Why should we assign probabilities to branches, and why do those probabilities coincide with the Born rule. My belief is that it won't be widely accepted until this is resolved. There are lots of (typically complex) attempts to derive the Born rule using decision theory or the like. There's no consensus that any of these attempts are compelling, or likely to succeed in the near future.