There's a cost to adding a dependency on Twisted. It's one more thing to download. There's more code to understand when something goes wrong. And so on.
What are the benefits to me as a web programmer? If I understand correctly, my application will work as it did before. If that's true, then Twisted did not add any win for me.
The benefits you get are seamless integration with all the other twisted tools and a solid foundation under the relatively new Tornado stack.
And a bug in twisted will raise many more eyebrows than a bug in Tornado - hence they are more likely to be discovered by someone else before you.
There's more code to understand
I criticize twisted for usability and documentation problems. But as the underpinning for something else (with hopefully better usability) it seems perfectly adequate.