I was thinking about this. It seems like a stretch to do a war, and maybe massive space battles or even important missions and not use your flagship in any of this. Trek already went with this problem once with the Enterprise-E not ever being used on DS9 for legal reasons of course. Might still be a legal issue since Pike and the Enterprise is part of the Kelvin Universe but it will feel strange from a creative angle to not see the Enterprise or at least get a reference about some big mission they are on that we the audience just can't see.
Jason
Jason