Hm, so you're saying that if |u> has high probability density in the subspace that contains Bob, then in the near future there must still be high probability density there, or at least nearby. But in fact |u> has very low probability density in Bob's Everett branch. Consider all the accidents of weather and history that led to Bob's birth, not to mention the quantum fluctuations that led to Bob's galaxy being created.
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.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.