You're overextending a hack intuition. "Existence", "measure", "probability density", "what you should anticipate", etc. aren't actually all the exact same thing once you get this technical. Specifically, I suspect you're trying to set the later based on one of the former, without knowing which one since you assume they are identical. I recommend learning UDT and deciding what you want agents with your input history to anticipate, or if that's not feasible just do the math and stop bothering to make the intuition fit.
Hm, so you're saying that anticipation isn't a primitive, it's just part of one's decision-making process. But isn't there a sense in which I ought to expect the Born rule to hold in ordinary circumstances? Call it a set of preferences that all humans share — we care about futures in proportion to the square of the modulus of their amplitude (in the universal wavefunction? in the successor state to our Everett branch?). Do you have an opinion on exactly how that preference works, and what sorts of decision problems it applies to?
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.