This is a altered time line so something that's a mix from different parts of the old show makes sense,and I think it looks good,no way just those shirts would be enough in some environments,the military does have stuff like the M65 before and whatever they use now.
One thing I HATED with a passion with the Next Generation was those stupid outfits,the coat I've seen Picard use later on looked like he stole it out of granny's dresser...and speaking of dresses...the hell was that dress/tunic thing from the first few seasons? what are they now? Romans?? but I have to admit the first Trek film in '79...those outfits were horrid in all their own way.
The new stuff looks good,look like actual uniforms.