In a block universe (eternalism) nothing emerges. Everything is eternal without change. However, this seems to go against our perception of reality.
But with a growing block universe, things become. The present emerges. This maybe just for the consciousness, or it might be that a new identity of the whole universe constantly emerges. Either way, new perceptions emerge, or the present emerges - something emerges!
Something seems to be emerging while much stays conserved.
A growing block universe assumes the existence of a universal now.
Relativity says that there's no such thing.
Personally I am not ready to ditch the extraordinarily well tested and robust theory of relativity, in order to keep open the possibility that an untested contradictory hypothesis might be true.
A growing block universe is attractive to many people for many reasons. That is completely irrelevant to its actual existence.
It seems to me that the universe must be a block universe; The many worlds interpretation would imply that the block has many branches, which might be a comfort to those unable to abandon their preferred concept of free will.
Personally I lean towards the idea that the future is fixed, but (for any given observer) unknowable. There's no need to get more complicated than that - although some more complicated possibilities (such as many worlds) certainly exist.
For sure we need to abandon those ideas that are not possible, if we care to actually work towards greater understanding of reality.