You are missing MWI's problem with the Born rule. If each "branch" exists only once, then all outcomes are equally probable, which is empirically wrong.
You keep asserting this, but you have not provided any good reason to believe it. Your assumption seems to be that the counting rule is the natural understanding of probability in MWI. I don't see this at all. As far as I can tell, there is no "natural" way to interpret probability in MWI.
Consider an analog: a Parfit-esque case of fission, where your body is disintegrated and, instantaneously, two atom-for-atom duplicates are produced in different parts of the world. Call these duplicates Mitchell-1 and Mitchell-2. It certainly does not seem natural to apply the counting rule and say that there is a 50% chance that you are now Mitchell-1. I fail to see why that would be the default position. The appropriate default position seems to be that probabilities are irrelevant here. I think that is the right default position in the MWI case as well, and it is incumbent on all proponents of probabilities in MWI to justify why one should be talking about probabilities at all. I can understand the criticism that talk of probabilites in MWI is incoherent, but I really don't understand the criticism that probabilities in MWI must be branch frequencies.
As far as I can see, the only way to justify talk of probabilities in the fission case (and, by extension, in MWI) is to think about it from the perspective of the agent's decision-making process prior to the fission. Perhaps even this is insufficient to get us any coherent notion of probabilities, but it seems like the only semi-plausible candidate. If you're going to justify the counting rule, you need to tell me why it would make sense for an agent in an Everettian world to organize expectations in accord with the counting rule. And this justification should not sneak in prior probabilistic ideas (like the idea that the agent is equally likely to end up in each future branch). Wallace claims to have provided such a justification for the Born rule. If you want me to take the counting rule seriously, I'd like to see an attempt at a similar justification.
It certainly does not seem natural to apply the counting rule and say that there is a 50% chance that you are now Mitchell-1.
Let's suppose I am to be disintegrated as you suggest, to be replaced with these atomic duplicates, Mitchell-1 and Mitchell-2. But we add that Mitchell-1 will be gunned down, and Mitchell-2 will not be.
Now suppose you ask me, before this disintegration, "what are the odds that a randomly selected future duplicate of yours will be one that is gunned down?" The answer is 50%.
But this is analogous to the situation in Many...
The subject has already been raised in this thread, but in a clumsy fashion. So here is a fresh new thread, where we can discuss, calmly and objectively, the pros and cons of the "Oxford" version of the Many Worlds interpretation of quantum mechanics.
This version of MWI is distinguished by two propositions. First, there is no definite number of "worlds" or "branches". They have a fuzzy, vague, approximate, definition-dependent existence. Second, the probability law of quantum mechanics (the Born rule) is to be obtained, not by counting the frequencies of events in the multiverse, but by an analysis of rational behavior in the multiverse. Normally, a prescription for rational behavior is obtained by maximizing expected utility, a quantity which is calculated by averaging "probability x utility" for each possible outcome of an action. In the Oxford school's "decision-theoretic" derivation of the Born rule, we somehow start with a ranking of actions that is deemed rational, then we "divide out" by the utilities, and obtain probabilities that were implicit in the original ranking.
I reject the two propositions. "Worlds" or "branches" can't be vague if they are to correspond to observed reality, because vagueness results from an object being dependent on observer definition, and the local portion of reality does not owe its existence to how we define anything; and the upside-down decision-theoretic derivation, if it ever works, must implicitly smuggle in the premises of probability theory in order to obtain its original rationality ranking.
Some references:
"Decoherence and Ontology: or, How I Learned to Stop Worrying and Love FAPP" by David Wallace. In this paper, Wallace says, for example, that the question "how many branches are there?" "does not... make sense", that the question "how many branches are there in which it is sunny?" is "a question which has no answer", "it is a non-question to ask how many [worlds]", etc.
"Quantum Probability from Decision Theory?" by Barnum et al. This is a rebuttal of the original argument (due to David Deutsch) that the Born rule can be justified by an analysis of multiverse rationality.