Cultures come and go, arising from circumstances that can change. Does preservation of a living culture take priority over the wellbeing of its members? Perhaps a culture is something that can be decommissioned humanely.
This is problematic. Who, but the members of a living culture, can determine any of these questions? My understanding is that most cultures are self-preserving, until they aren't, usually through conquest or other external forms of eradication.
I don't see the problematic aspect of "curing" the child's deafness before they become a member of the Deaf community. It's not removing someone from the Deaf community. Deontologically, it ought to be fine, surely? (I'm looking at this deontologically, because from a utilitarian perspective, we should be asking what is the correct percentage of otherwise non-deaf children we should surgically make Deaf.)
Because you do have such a threshold, and you consider things that fall below that threshold not to be "culture", and therefore not to be worth preserving.
Which leads to: How do you justify this choice of threshold?
Nihilism is perfectly fine as a philosophical argument, but few would support it in practice
I agree that your reductio ad absurdum argument shows that "nothing deserves to continue" is in untenable position. But surely the opposite extreme (namely, "everything deserves to continue") is just as absurd?
So the question remains: Where to draw the line?