You are being unreasonable.
For starters it's not like Zoro can decide what his character will do, Oda decides that and he decided that Zoro had to got stop the birdcage, so all that stuff about him still being in his 'tux' and him being lost is completely nonsensical. Oda would really not have let Zoro do that if it was Zoro who had to do it or in another interpretation that Zoro should not be close to Luffy like for example to have Sabo protect Luffy. A different possibility is that Zoro should not be fighting DD in the condition the latter is. Luffy said that one more heavy attack would be enough to beat DD and Oda has always been very careful when it comes down to making a pecking order among characters and especially among the Strawhats. Having Zoro just stall DD for 10 minutes means as much that Zoro would not be able to beat DD who is is severely injured and one strong attack away from defeat while Zoro has not yet used all of his most powerful attacks and is in decent physical condition. Having him beat DD on the other hand doesn't make sense either. So how solving that problem? By sending him away to do something else as it's Luffy who needs to deal the finishing blow. That also might be the reason as why he is letting Sabo fight Burgess as at this point I can only see three characters, outside Luffy, who could launch an attack powerful enough to beat DD: Fujitora, Zoro and Sabo. Fujitora is not going to intervene due to complexity of the situation. If he could, he would have done so already, zo Oda made sure that both of the others were occupied.
Secondly Zoro did more than enough. If Zoro hadn't beaten Pica, several Strawhats would have died alongside many of their allies and civilians of Dressrosa. Then Luffy's chances of beating DD would have dropped likewise to zero as it's highly questionable he would have been able to beat both DD and Pica. I doubt that Usopp is going to say to Zoro he did nothing when Zoro avoided him being flattened like a pancake.
Thirdly if Franky alone would be able to destroy that cage, that cage would already have been gone, then it would really have never been much of a threat. Even Fujitora's attack was ineffective and considering the nature of the bird cage, Zoro is probably the most suitable to do it. Zoro is not the type to take half measures, he is not planning to push back the cage, but to destroy it and that in itself is also aiding Luffy as by now all the people are being gathered at the spot where Luffy is fighting, which only works against Luffy as DD doesn't care how many people die. That cage is a time limit and it's pointless for Luffy to win when in the end everyone got shredded to pieces. So destroying it is also helping Luffy.
