I liken the Discovery crew to immigrants. Except instead of immigrating to another country in another continent, they've immigrated to another time. And they can't go back because of the situation. Not an uncommon issue with immigrants, depending on where it is they've immigrated from. Including within my own family. It's complicated. As is the case more often than people who don't have to deal with this might realize.
The crew have made their lives in the 32nd Century. So, I think they've accepted this is where they are now. Also, if you're going into space and leaving your home life behind, you're someone who wanted to get out and get away to begin with. Or maybe they don't have much to go back to.
To quote Star Trek V (yeah, yeah, yeah, I know, it doesn't matter what you think of the movie, that isn't the point), anyway, to quote Star Trek V: "All that time in space, getting on each other's nerves, and what do we do when Shore Leave comes along? We spend it together. Other people have families." "Other people, Bones, not us." Then cut to the end of the film. "I lost a brother once. I was lucky to get him back." "I thought you said men like us don't have families." "I was wrong."
I think this would've been an interesting thing to explore in third season. But, in the fifth season, it's too far after the fact. I think the Discovery crew views each other as their family. Being the only people they know who came from where they did and making the leap together.
Outside of that: Tilly hated her family. I think she's made a life for herself teaching at the Academy (I'm betting S5 takes place between semesters), Saru's got his career and he's with T'Rina, and Burnham has her career and she's with Book. So, they left their old lives behind (Saru's done it twice), but they have new lives now.
If SFA takes place in the 32nd Century, and the 32nd Century doesn't stop with DSC, then there might be other Star Trek series that take place there. So, I'd like for the opportunity for these characters to still show up. That's another reason why I want closure but not total finality.