What does leading the family even mean?
Basically all of them are anyway doing their own stuff, maybe with the only exception of Cassandra and Stephanie, who are allready working with Barbara. Batman has iirc not really lead anyone since the end of the last Outsiders series.
Comes to me more of like the writers want to validate Dick and Barbara for no good reason.
Btw. at this point I'm really wondering how the Batfamily afford their stuff (or even just their normal expenses).
Bruce and Barbara have lost their money, Dick seem to haven given all the money he got from Alfred to a foundation (because buying Superhero Gadgets is a bad use of money). And Bruce seem to have lost most his stocks after this.
I guess Jason might still have some money and some weapon stocks somewhere, but I doubt the other really want to use the kind of weapon he has stored.
Helena might also still have some of her mafia money, but currently it also didn't look like she is that rich anymoe.
And Tim, Cass, Steph and Duke don't really have much money on their own.
So unless Kate or Luke are suppling the others, I'm not sure how they should keep going.