If you are integrating an existing web application, Twisted has interface libraries for Django and Flask. You can also integrate with all the same SQL and NoSQL databases like MySQL, PostgreSQL and MongoDB.
Twisted gives Python an organized way to handle events in parallel and asynchronously, something the native Python environment was not designed to do. This gives you the ability to serve your existing Python code in a way that allows the use of modern web services like Web Sockets. This can allow your web applications to operate more efficiently, integrate with legacy systems that were not designed with web servers in mind, and provide a much more responsive user experience.
You get access to all the cutting-edge Python libraries in a unique runtime environment that can help you get an existing project running more efficiently, or help you extend your project to support new, secure, more responsive features.
Twisted requires a different design philosophy than regular Python developers might be used to. If they have only used Python to develop web applications with frameworks like Django, they may struggle to use Twisted effectively. This is where hiring developers with previous experience can help you get a product out quickly, and help introduce your in-house developers to new technology without the expensive learning curve.