Well DSC has proven you don't really need to keep the canonistas happy to have a hit show. Actually not really letting them dictate your show's visuals is probably why this show has more mainstream appeal.
I agree but it does make you wonder why they even pretend to be a prime universe show. They must think fans will either believe anything they say at face value or that the Kelvin Universe movies are really,really unpopular and they have to constantly remind people this show is not set in that universe or that people simply have no idea of other alternate timelines or that the reboot word is now a nasty word unless it is sort of connected to the old show or movie. Even the Kelvin Universe made sure to have Nimoy's Spock to create a connection while also comforting old school fans that everyone they grew up with didn't all of sudden cease to exist because of time travel.
It could also simply because Fuller wanted a more traditional look, mentioned the show was in the prime universe and you can't just come in and say he was wrong or we are doing away with his plans. I'm not even sure CBS as owned up to them firing him. I don't think they want the audience to know just how much interference was going on back then. That's for future "tell all" books.
Jason