Agile isn't right for all software projects. For example, mission critical applications, like medical devices, shouldn't be developed with an agile methodology. Agile is better suited for projects that can be easily and appropriately prototyped.
The worst case is millions of dollars spent to build a product only to discover that there are issues late in the testing phase. Wouldn't is be less risky to experiment and validate assumptions earlier in the cycle?
Agile as opposed to methodology X is a bit fuzzy here, as I'm sure testing is extensive and expensive and the feedback cycle is inherently longer, so change is more expensive.
However, it seems that early feedback and validation of design is even more important in these circumstances, since changes late in the product development process and orders of magnitude more expensive than changes early in the process.