Harping on accents is pretty pointless because it's so arbitrary. Why doesn't Worf speak with a Russian accent? Why does French Picard speak like a Brit? Why do we see so few humans on the Enterprise with anything other than a regular, non-southern, non-New York type, etc American accent? At least with Trip on ENT you could tell he was from the southern U.S. Why doesn't Mr Mot speak with some kind of accent? Why do many aliens sound like they spoke english all their lives?
Yeah, it's insanity to dive down into the accent rabbit hole. Best to just leave that alone and roll with it.
It nags at me because attention was drawn to it specifically, in the dialogue. It would have been easy enough to mention that Deanna had picked it up from her father (until we learned he didn't speak with that accent) or if she'd spent a significant amount of time somewhere that the people do speak like that.
An example of an in-universe explanation of multi-family accents is the 1984 Lynch movie (Dune). Leto, Jessica, and Paul all have different accents. It's easy enough to head-canon it as Leto speaks with a Caladan accent (born there), Jessica speaks with a Wallach IX accent (one of the Bene Gesserit chapterhouse worlds), and Paul spent so much of his life with servants and retainers like Duncan Idaho that he picked up their accent.
So why didn't the showrunner drop a line in somewhere to explain Deanna's accent? After all, we the audience were basically told that even Deanna's mother considers her accent unpleasant, and something she should have "lost."
The complaints about Patrick Stewart having a French family who speak with a British accent is ridiculously easy to explain, given the millennia-plus of interaction between England and France. We don't know the precise political boundaries of 24th-century Earth, and because I'm familiar with the broader scope of history (and the linguistic influences when invaders come and go), this part of the show doesn't bother me.
Worf likely could speak Russian if he had a reason to. But he doesn't, at least not on the ship, and it's not like he had zero exposure to Klingon languages in his childhood. Note that he doesn't use slang much, and he speaks in a more formal way, as someone might whose first language is not what might be considered the 24th century equivalent of standard English.