But that doesn't mean that there shouldn't be a continuity. And honestly, I don't know if I buy that argument that continuity-enabled ramifications don't fit the way audiences work today. I mean, pretty much any franchise is made popular not because the characters are just "kewl" but because of the lore behind the characters. Batman isn't just a guy who dresses up in a bat-suit without a past. That's just an idea, not a character. The character has been through events and storylines that have defined who he is as a character and his world around him: Year One, Joker's Five-Way Revenge, Death in the Family, Knightfall, No Man's Land, Fugitive, etc., etc., etc. These are all the stories that contribute to a mythos that contribute to a franchise. That's as true today as it was 50/60/70 years ago.
Well, not really. Because, while Harley Quinn and Carrie Kelly may not have been created in the main DC continuity, they were still products of continuity. They were born out of the continuities of their respective worlds: the DCAU for Harley and the Dark Knight Returns continuity for Carrie. Carrie's story doesn't make sense without the set up of DKR. She doesn't make sense as a character without that world around her, where Batman has long retired and Gotham has turned into a cesspool. The same thing goes for Harley. And it should also say something how Harley's popularity spurred them to bring her into the main continuity, but at the same time, DCAU Harley is not the same as main DCU Harley. Those are two different characters and the realities of the DCU have made Harley evolve into who she is today.3. Yes, but you can still create popular characters without resorting to needing continuity. Carrie Kelly and Harley Quinn for example. Plus the fact that these characters can't and in my opinion shouldn't grow old and retire or die means eventually all that mythos gets squeezed into an impossibly short time - I'm sorry but Batman just shouldn't be in his 50s to me.
Plus, even if you don't think Bruce should be north of 50, that doesn't mean he should be in his 20s either. Like, honestly, I don't buy a Bruce Wayne in his 20s. The maturity, authority, and reputation the character demands requires him to be in his late 30s at least. You don't build up a reputation as "the goddamn Batman" when you're like 25. You have that reputation when you have some years under your belt.