It lessens the story for me. It ruins my suspension of belief. And, cynically, often the connections seem to be forced in for "shock" value or economic reasons when other, better, new options exist. It also restricts the story - no longer is there a fresh and new opportunity to explore - now the writers are beholden to existing characterization and histories. Or they're forced to re-write said characterizations and histories to tell new stories, rendering the point of connecting to existing characters moot.
Discovery promised new ships and new crews. A week from filming and of the few characters reveals, we've already got one who has been described as key and has already been in three TV series' and two film franchises spawning 50 real time years. That's hardly new.
Hence my disappointment.
I'm well aware a lot of people disagree on this, that's the nature of art. I'm not arguing that you or
@Balok's Decoy or any of the others excited for the connection are wrong - it just doesn't work for me and seems a waste of a new opportunity to body go where no one has gone before.