Yea Carroll has rather the obsession with Boltzmanns brains. Both sides have vaild arguments if we were living in a boltzmann brain dominated universe random observations would be more likely but no amount of measuring would prove that you weren't a boltzmann brain.

Of course Carroll repeatedly tries to use this to argue agaist a universe dominated by boltzmann brains, but it does no such thing all it means is that he WANTS the universe not to be dominated by boltzmann brains because if it is then his life work was a waste of time :P

"Very improbable" is the typical assumption with MWI, but I think that it is mistaken in most cases dealing with complex systems.

Each wave-function sets limits on what can occur. Wave-functions don't have infinite extents, there are areas with zero amplitude. Each additional wave-function that must meet specific requirements further restricts the possible outcomes. In general, the likelihood of failing to meet the simultaneous condition grows exponentially as the system size grows linearly.

Since quantum survival (avoiding death in some worlds, in some meaningful context) will usually require a very large number of quantum level alternatives to be simultaneously selected for, quantum survival will almost always be impossible.

A person who experiences quantum survival once is very lucky, but almost certainly won't survive the next time. A person who fails to experience quantum survival never gets another chance.

So my conclusion is that quantum immortality is impossible, not just very improbable.

Your logic here makes no rational sense. Your saying things which can be proved to be false.

Firstly I accept your premise that some things have zero probability. The wave-function doesn't mean literally anything can happen

BUT

I strongly disagree with you when you start saying that simultaneously selecting for possible (but improbable things) makes them impossible because this makes no rational sense. Quantum events are independent of each other the fact that 1 radioactive atom decays doesn't mean that the next is more or less likely to (unless they interact of course but I am ignroring that) nor is there a cutoff as to how many atoms can decay.

If a random event has a non zero probability of occurring, then a googleplex number of those events has a nonzero probability of occurring, in ANY COMBINATION.

I am a mathematical biologist, have a think about how many random mutations had to occur to create you.