Then they just need to stop claiming it to be "still the Prime Timeline/Universe" if its obviously not, as evidenced by recasts and changed backstories.
It is very obviously NOT set in the original 60s continuity, regardless of what any producers or any fan insistence claims. Not sure how it is a "fannish" notion when it is blatantly made clear by just about every choice the producers have made.
No. It's all the same fictional universe if the creators of that fiction say it is, because they own that fiction and you and I do not. Things can be set in the same universe and also have inconsistencies, because this is all make-believe and consistency is not required for them to be set in the same continuity.
The producers insistence that it is prime is the only thing that can make it prime. The idea that inconsistency, recasts or change negates it being "prime" is a fannish notion. The franchise's history is rife with all three and for some reason only recently have fans decided to declare things "not prime" for them.
Exactly. It's the application of conspiracy theorist thinking to make-believe. There is no "real" Star Trek Universe for productions to be consistent with, and people kind of ignore that.