The way they’re doing the Discovery version of the Enterprise would have been tolerable.
What they did not only to the design of the Klingons but their culture as well in season 1 absolutely precludes it being part of the Prime Timeline.
And that’s ignoring the ridiculous Star Wars holograms throughout the series.
They could never make Discovery if they were beholden to the aesthetic of the 60s, but some people don’t want a change in precedence.
And that’s why it shouldn’t have been set when it’s set. Nothing about it aside from who her adopted parents are necessitate it being set pre-TOS.
And if they really wanted her tied to Vulcan they could have made her Spock’s adopted daughter instead of sister.