You're talking about the after effects of an attack mate. Even if the birdcage is destroyed or stopped then damage done by it and the strings used to create the cage will stay there just like how lower part of Pica's statue didn't collapse even when Pica was defeated.. It's the same with Akainu and Aokiji. Akainu can create dog like structure with his power and make it go after his enemy but can it be done automatically without his involvement? Going by your Akainu and Aokiji logic the bird cage won't disappear even after the defeat of Joker but it'll lose it;'s meaning and becomes nothing but strings with no mobility. Once again no devils fruit power in manga was hinted to be able automatically attack enemies without any involvement from the user.
Zoro said that because he knew that an attack from a fruit user will be stopped as soon as the user gets defeated. Look at Sugar for example. If law made his rook and someone KO him then the rom will obviously disappear , similarly BC will be stopped as soon as Joker gets defeated.
If Luffy defeats Joker and still won't be able to stop BC then it's be lame as hell as it won't be Luffy that'll completely put an end to Joker's evil actions. Luffy had already addressed BC while fighting Joker and said he's going to stop both so if says that he's going to do something then he'll do it without a question.
Joker has yet to use a decent attack via his awakening. Look at Luffy he entered G4 and is using multiple kind of attacks and why can't Joker do the same? All Joker did for 20 mins was trying go after Luffy and getting dodged so I doubt Oda would introduce this whole awakening crap and make it lose that easily.
Oda just loves to play with us readers. We are getting excited and all because we don't know what's going on and that's what Oda wanted to do. Remember when Law was claimed to be dead and look at what happened to him. It's the same with Luffy's battle. As I said before an ending without epic movements isn't an ending in Oda's manga. Trust me , the fight is far from over.When Luffy defeats Joker there will be cheerful movements, lots of sentiment, crying faces,exciting faces,happy faces, fanboy movements and WTF? faces from people that have no idea about the situation. Bartho will most likely die from heartattack.