Jonathan Frakes mentions several things in the TrekMovie interview that may impact costs.

Alex Kurztman set the direction style with more close up, tight camera work. More, he specifically ordered special long camera lenses to enable that. This means that despite the enormous sets and UHD cinematography, with long lenses they are able to block the scenes without as much extraneous detail.

Saving the wide angles for when they need them but closing up on the characters, and doing more in set internal volumes must surely reduce a lot of crew time and accelerate production.

Announcing Becky Lynch only to use her an an extra twice, doesn't feel like cost cutting as much as a potential breach of contract.