It's as much Star Trek as the unofficial Trek movie Galaxy Quest. Doesn't matter if the characters and universe are different, it's got the same vibe to fit in.
I can understand why. The motivations and message are a bit deeper than WoK. But UC wouldn't have happened (in the same way) without WoK first, since I don't think Kirk had the same hatred towards Klingons before. Distrust sure, but not revenge level hate.
UC also has that connection with one of the best TNG episodes, Yesterday's Enterprise.
Honestly I kind of wanted them to keep more of the humorous tone. I know a lot of people hated it and thought it was distracting, but I thought it was a pretty unique take on the genre. I wish they'd toned it down without going full space opera.
I think the humour in the first few episodes was Mcfarlens way of sneaking the show past the network suits - he sold it as family guy meets star trek, then switched on them once it was established.
Literally the case, the first couple eps were written for fartjock executives. Ep 4 onwards were written for the show. It's why there's a sudden stratospheric upswing