I think when discussing how big or small the Bat Family should be, one must consider if these characters have a purpose, an arc, or a role to play in the life and mission of what was originally a street-level detective in a scary costume. Not just “are they a female counterpart” or are they “the rebel” or some other cliched non-trait. For certain characters, I’ll be omitting their reinventions (and not just because those reinventions sucked eggs).
(Okay, mostly because those reinventions sucked eggs.)
Alfred - He patches up the wounded, works on some of the machinery (computerized and otherwise) and helps with keeping identities secret. He’s a father figure for most everyone, helping keep them grounded when they spend so much time punching guys in clown masks or fighting hypnotized office workers. He has a purpose.
Nightwing - The original sidekick, old enough know better, still too young to care. He identifies with Bruce because he had the same tragedy and the same drive to see justice done. He’s like if Batman was more trusting–and had a clearer sense of humor. Experienced enough to teach his younger counterparts a thing or two, but with some things left to learn. He has purpose.
Barbara/Oracle/Batgirl - Someone who kind of “happened” into crime-fighting. There was a thrill-seeking element at first, but she grew to take it more seriously. She can wallop baddies physically, but she can also ruin them in other ways with her keen hacking abilities. She can fight on a different front, with her mind, while others are using their fists. Much like Grayson, she can be a mentor to the younger heroes, guiding them. She has purpose.
Tim Drake - A deductive prodigy; a capable fighter but his mind can be sharper than others. He didn’t join the fight because of an epic tragedy, but because Batman needed someone at his side to ground him, keep him from going too far. He probably could’ve kept Wayne’s secret forever, if the loss of Jason Todd didn’t drive him to the brink, but an inherent goodness drove him to become the third Robin. As someone that is doing good because it is good and not because of an epic tragedy, something altogether rare in comics, he has purpose.
Stephanie Brown - Personally affected by crime, she strove to personally ruin her father’s ambition (remember, I’m omitting the post-Flashpoint iterations). She felt she had more to offer, she could help more people despite her inexperience, and wanted the chance to prove it. But time and time again, she kept being told to quit, for years. However, she remained resolute; she met rejection with tenacity, in the face of someone whose pointy-eared silhouette makes criminals afraid, again without some blood-stained motivator. She has purpose.
Cassandra Cain (not Orphan, because obviously) - It’s one thing to crusade against crime because it caused a tragedy in your life. It’s something else when you know from firsthand experience. Uniquely aware of what it was like to take a life, Cass had an equally unique understanding of what Batman is striving for, all the while possessing the skills to defeat nearly anyone. Immense, powerful ferocity, kept in check by compassion and a desire for redemption. She has purpose (when written by someone competent and frikkin’ editors aren’t being stupid).
Damien Wayne - Yeah, this one’s kind of a jerk. However, they still keep Guy in the GL Corps, right? He wears his ego on his sleeve. And cape. And shirt. And pants. Abrasive, but being the son of Batman and raised by an immortal grampa to believe he’s all that and an entire factory of chips, he has a lot of growing up to do, even if he can match his predecessors in physical combat. He presents a blood connection to Bruce that was much scarcer pre52, a sign of the future generation that must temper his ego if he is truly to succeed the Dark Knight. He has purpose, if more tenuously than others. Call this one a grey area, maybe depending on the writer.
Duke Thomas - I don’t know or remember enough about him to say for sure. He met Bats when he first appeared in Gotham, made the connection he was Bruce Wayne, started his own Robin group–none of which is bad, per se, but I can’t say for certain whether or not it proves a role in being in “the family”. Note, he can work with Batman, be a valid character, and not be in “the family”. Kind of like Huntress, Catwoman, or depending on your perspective, Steph Brown.
Harper Row - A conglomeration of traits and skills other sidekicks had before her, wrapped up in one of the least likeable packages imaginable. I don’t care how badly Tynion wanted her to be the bat-messiah, she serves zero purpose. To anyone. Ever. If she were killed off, she wouldn’t even be as effective a cautionary tale as Jason Todd, because she never did anything noteworthy or important.
Batwoman - Again, I don’t know enough about this character to determine this. I actually liked that she, as indicated by Babs in Batman Eternal wasn’t "in the family, but then they made her Bruce’s cousin for some reason. I have no idea why; It didn’t seem to add much to either character. Personally, I feel like it kind of means more if Bats kind of seeks or gains a family outside bloodlines, but that’s me.
Red Hood - Batman’s greatest failure, the Robin he lost–then got back again, only angrier and with a pair of glocks and matching itchy trigger fingers. The Bat’s skills in the hands of an angry man who’s not above killing his foes and getting his hands dirtier than most. He serves a purpose–but, I feel, only as the disowned family member. Sure, he towed the line for a while, but decided to forsake his mentor’s ways and thus, exiled himself from the clan. It makes more sense if he’s at odds with his “siblings” than if they’re all buddy-buddy with someone that spits in the face of what they work for. “Look at me, I’m the cool older brother that’s not the oldest, and I break the rules, but it’s okay because of things and reasons! Wooo!”
Clayface - Ha! That’s a good one–wait, you were serious? Seriously serious? I mean, no way was his turn going to last. Heck, I’d wager it was only done for that big weepy dramatic “death” that was also never going to stick. I mean, no, obviously. Not Clayface. Heh heh. No.