Many Rails apps are tightly coupled, and many unit tests written by developers using rails test 10% program logic and 90% framework features.
Of course this is going to be slow. We can argue about hacks to make it faster but at a certain point it's a problem whose solutions start to distract us from solving the important problems.
If you have a web app and get to write a single test to determine whether it's safe to deploy, that test would be an integration test.
The decision to write tests more granular than integration tests is a decision to be made based on assumptions about the rate of change of components of the system.
TDD is tangential to the above observation.
There are many cases where an implementation is easy to figure out (though possibly time consuming) while the optimal interface design is less obvious. TDD can be really useful to quickly iterate interfaces and verify that all the moving parts work as expected together, before worrying about the implementation details... This makes it possible to work on a larger system with more focus on problem solving, fewer mistakes, and less overall cognitive load.