As far as I can tell New Zealand is a Church of England based state and has never undergone separation. In state ceremonies prayers are said and oaths to God are made – no one is wronged by this aspect of church and state integration.
The doctrine of separation of church and state is supposed to avoid religious persecution, state forced indoctrination and state suppression of beliefs however some of the worst persecutors of religious people and indoctrinators have been secular states.
NZ state schools suppress religion due to separation considerations but state indoctrination (Treaty of Waitangi, Global Warming, naturalism, etc.) is compulsory. And in NZ people can be persecuted for their beliefs using the Bill of Rights. These wrongs however do not stem from NZ’s integration of church and state.
The doctrine of separation of church and state doesn’t stop religious persecution, state forced indoctrination or state suppression of beliefs.
The doctrine of separation of church and state seems as likely to cause the problems it is supposed to alleviate.