Fujitora hasn't been shown reacting to the shrinkage yet. He was trying to gather all the townspeople in one place for a reason, presumably to use his gravity to protect them all at once.
Besides, even if Zoro or Fujitora can slice the Birdcage up, what's to stop Doflamingo from creating another one? The only true way to get rid of the Birdcage is to stop Doflamingo.
I mean Fuji attempted a meteor before, right? Or was it anime-only scene? I forgot. I'm curious to if gravity will work on these strings. And if yes, he should have used it way earlier before now, or since after the meteor didn't work on the cage.
Anyway, these strings may be too ridiculous sturdy material. I bet Akainu's lava wouldn't melt it either the way these strings have been shown to be so far.
–- Update From New Post Merge ---
After this, Dressrosa got a lot of clean ups and a massive repairs to make after getting battered up.
Pica literally changed the structures and also destroyed some (actually more than some).
"a lot of clean ups and a massive repairs" is still an understatement.