Why would he mention it? She was born nearly 300 years after he left, she's 10 generations removed. It would've added anything or even meant anything to Khan other than he has descendants who hated him.
Having her as Khan's descendent is a bad idea I think unless you agree with me that this is an alternate reality. Kirk and Spock had to look up all about Khan as they didn't immediately recognise him from seeing him in the Botany Bay only Marla McGivers did and that was because she was a student of history and had always found him desirable! Yet here we have a woman discussing her ancestor, Khan, hating that she was related to him with her superior (Number One) and she knew of him straight away, almost as if his attempted conquests were more recent than three centuries earlier!!! JB
It's not a bad idea; It's not an "alternate reality.*" Having disposed of that... In the slightly-less media-saturated environment of 1966, back when it seemed plausible that there might be a Eugenics War in the 1990s,** having characters not recognize an individual by sight from 300 years previously didn't seem that unrealistic. It's not as if Khan Noonien Singh as an historical figure was obscure or unknown to Kirk and his crew, either - they were a little fuzzy on the details, but they all knew who he was and more or less what he'd done. Indeed, Kirk, Spock, Scotty and McCoy all had personal opinions about him when he was first brought up. *Bullshit terminology for fiction, IMO. **It's in the 21st century ahead for now, kids.
Yes that's true they did but could any of us recognise a despot from the seventeenth century today and would his actions have still been of great interest to us today? JB
And it has to be an alternate timeline if you want to keep TOS as a possible future to these new shows! JB
Recognize? Probably not, especially with photography being limited. Of interest? Um, absolutely. I study leaders and despots older than that.