1. Much less time spent trying to chase requirements that are technically infeasible within the budget and rough timescales. This on its own normally more than makes up for iterating and throwing away proof of concept implementations of features.

2. Much better visibility of progress. Because you are delivering something tangible that stakeholders can see and feel all the way through the development process, you get better feedback from your stakeholders, better buy-in from your sponsors, and fewer canceled projects.

3. Where projects are canceled, they tend to be canceled early where they are clearly not working, before millions has been spent.

The need for requirements doesn't go away with agile. If you start a project with no requirements, it will almost certainly fail. However the iterative process allows you to refine the requirements as you go, and the early and frequent feedback from your stakeholders makes the requirements better. It's easier to add or remove a requirement if you can see the software doing something wrong or not doing something it should do, rather than trying to figure it out on paper ahead of time.