Nobody forced them to use the TOS crew. They could have invented a new crew with more women, homosexuals, Muslims, Aborigenes and everyone else who feels underrepresented in modern media.
They made a choice not to use the established TOS characters that would have fitted into the story, namely: Number One, Rand, T'Pau, and Chapel (who only gets a name check).
My issue isn't so much with the main cast they DID use (although I'd have been happy if they'd saved Chekov until later) it's more with the supportng cast that they left out and the new characters that they introduced. I would do Robeau given half a chance but he wasn't exactly an equal opportunities employer. Very uninspired casting overall.
I mean, I loved the Worm that Turned in the Two Ronnies but they weren't claiming to espouse equality. I just want to Trek to live it rather than just talk about it.