I think that there can never be infinite different worlds because they would blow each other up. The logic chain goes something like this:
There are infinite different worlds
Each world is different
There are infinite differences
Each world has different possibilities
Thus, anything is possible
Therefore, it is possible for a "reality bomb" to randomly appear and detonate
A "reality bomb" is unstoppable and will spread forever, seeping into dimensions, universes, matter, anti-matter, logic, mathematics, the "ideal" world, the "real" world, and everything real and unreal.
Thus everything will be destroyed in 0.000... seconds as soon as there are infinite different worlds
Hence, infinite worlds=all worlds are destroyed
Therefore, any world you find yourself in must be one of a limited number
Because if you are reading this, your universe/surroundings must still exist.
5 is a non sequitur. Just because there are infinitely many worlds, each with different possibilities, doesn't mean that anything is possible. The set of integers can be partitioned into infinitely many disjoint subsets, but none of them will contain π.
The important thing you are missing, and is also germane to Boltzmann brain arguments, is the mathematical concept measure. There may be infinite reality-bomb universes, but also infinite not-reality bomb universes. The ratio of these possibilities is what's important.
Leonard Susskind in this lecture says an infinite multiverse via eternal inflation can still explain why we exist and why we don't see BB's, even if infinite of them collapse/explode. More do not collapse/explode because the chance each daughter universe spawns a daughter universe is greater than the chance of one imploding (or spawning BB's).