The problem with that is that it's definitely stated to be a keel-up refit in the first film. It's the same ship but explicitly stated to have been radically altered.

Captain America: The First Avenger had a pretty solid budget, but that didn't mean they threw 2018 Camaros around the 1940s scenes.

That's part of it. The other part of it is they're running a bait-and-switch. "10 years before Kirk, Spock, and McCoy on the Enterprise!"

Then that's the challenge CBS set for themselves when they decided to set it 10 years prior to TOS.

Quote: "…(remember, Discovery takes place 10 years before The Original Series)."