Testing different methods of development in terms of speed, cost and quality is really hard. The most convincing approach to me would be a single blind experiment to hire two software development teams and have them build to the same set of requirements in two different ways. But then it is hard to know whether you are really comparing the method of software development or the quality of the software teams. So two software teams isn't enough to get a statistically valid inference. You can see that, given software development rates, this could become a very expensive experiment.
Last point. I think that even writing a specification down to the level that it could be implemented using formal methods might be the biggest game changer. Agile stories rarely come even close to covering all of the potential edge cases. If we had a process that required product owners to literally think through all possible failure modes (what systems of formal methods do) and write out how to handle them then the cost of writing specifications would go way up. Per economics, I think we would end-up with simpler specifications which might be its own benefit.
Last point. I think that even writing a specification down to the level that it could be implemented using formal methods might be the biggest game changer. Agile stories rarely come even close to covering all of the potential edge cases. If we had a process that required product owners to literally think through all possible failure modes (what systems of formal methods do) and write out how to handle them then the cost of writing specifications would go way up. Per economics, I think we would end-up with simpler specifications which might be its own benefit.