if the set of nested universes really does look like a funny graph of bubbles, i think there are two likely possibilities: either the set of bubbles rapidly dries up, or it grows towards infinity; in which case, if compute is infinite as wolfram would have me think then as soon as the bubble explosion happens, it's likely a universal complete algorithm is booted somewhere reasonably fast, itself booting in turn all initial states.
this has the result of instanciating all (countable, discrete) tegmark 4 universes, over time.
yet, we still observe a preference for coherency: i think the reasonablest interpretation of what'd be going on is that "computationally early" or at least "computationall frequent" states are favored; and thus, very weird and incoherent initial-state universes do get spawned, but much later and/or are being computed more slowly (for example, maybe computation is equally distributed among all timelines, and as more and more timelines spawn over time each individual one gets updated less and less often).
while this creates a neat explanation for what selects for universe coherence, it does make it that while quantum immortality/suicide can be considered to "still work", if you choose to keep living only by waiting to be reincarnated later, you're reducing the "realness" of your continued existence; you're making universes in which you continue to live appear only "computationally later".
it also provides a nice simplicity test fo roccam's razor: the simplicity of a hypothesis can be akin to how soon a universal-complete program that simulates all spawned computations arrives at it.
this probly doesn't apply to "classical" quantum immortality where you just use the fact that you're redundanced on other timelines, because i would imagine those other you's in other timelines would tend to be computed "at the same time".