Red Robin’s comic moved past the search for Bruce after the intial arc, and most definitely embraced Tim’s civilian life for the bulk of its run as a solo comic.
And I disagree with disparaging character concepts in the Bat-Family... largely because it’s an excercise in double standards and biases from everyone. I mean, Tim’s “just” as much an unoriginal character as Jason is... but both characters prospered in days and ages where they were given books and runs with support from editorial when other characters weren’t and had creators figure out their individual formulas. There are plenty of things both character do that could, in theory be done with other characters... but the failure of such attempts at times puts the lie to that theory on practice. “Ric” Grayson was an attempt to make Nightwing act more like Red Hood. It failed. New 52 Teen Titans desperately wanted Tim to be Dick. It didn’t work. DC Pre-Flashpoint kept on trying to make Jason fit in an AzBat-style “evil Batman” role, even with Morrison’s Red Hood repackaging. You don’t see anyone howling for that to come back.
Jason’s “just” a 90’s throwback action hero, in the same way Damian’s “just” a Mary Sue, in the same way that Babs is Batgirl “just” because she was in the 60’s Tv show, in the same way Tim’s “just” a Spider-man-as-a-Batman character, etc...
None of that’s actually true. These characters are ridiculously successful in the right hands. And all of them have had the wrong hands applied as well... and yet as comic properties, many of them would be judged as more valuable than some of the Justice League characters.
As to the redundancy factor... I actually think the Bat books have largely disproved that notion whenever they’ve had multiple characters heading series, while most of the times that they’ve been denied that opportunity, it wasn’t because of any failing on a book’s part - it was editorial chasing a dubious marketing theory that usually didn't pan out. Robin, Red Hood, and Nightwing have all generally run alongside one or the other, in spite of being largely the same concept of an “autonomous sidekick spin-off” - and it’s not like Dc shied away from having Damian headline books as well doing those times. Batgirl and Batwoman weren’t eating into each other’s sales - Batwoman’s fall was precipitated by editorial shooting itself in the foot by cancelling a marriage.
Which ties into this thing:
Very rarely has a once-successful Bat-family spin-off been cancelled just because the character couldn’t “sustain their own book,” but especially regarding the common suspects here.
Cass’s book was cancelled because editorial didn’t think the fanbase was ready for two Bat-female books with Batwoman’s appearance intended to arrive (which ironically got delayed). Tim’s book got cancelled because they wanted to try fusing his fanbase to their New 52 Teen Titans book, which they were so dead-set on trying to make work they wound up restarting it without any major changes. Steph’s book also got axed by the New 52, and while her monthly sales were low, her TPB sales were disproportionately strong and something DC hoped to replicate elsewhere; her series ended more because editorial again didn’t think that Babs would sell if Steph was admitted to exist.
There’s also been times where sales had the floor dropped underneath them, or where support never really became as strong as hoped for, but editorial/other creators’ faith in the concept lead to long runs and relaunches.
Catwoman’s 90’s series tanked for a while after NML... and then they took the character off the shelf for a while, repackaged her with Brubaker and Cooke, and printed money. Nightwing was in a dark spot around the War Games/Infinite Crisis spot, and Didio wanted him dead... and then Johns and others rebelled, soared him, and a few years later he was a successful Batman. Red Hood has never really been anywhere near the producer that Nightwing or a Robin are... but DC editorial smartly realized he had a reliably dedicated fanbase and that he was the one character Scott Lobdell seemed to not drive people away from as a headliner, and just repacked the book multiple times.
The Bat-Family characters aren’t liabilities to each other; they’re assets.
There need to be less infighting and fear of “redundancy” and more an embracing of the large cast. It’s not like it’s stopped Batman from having solo adventures.