Experiments are pretty damn crucial to the entire scientific process, right? What if you couldn't do controlled experiments? That's where economics is right now. Until we either get enough data or economists can run actual experiments (ie those that don't just rely on fabricated mathematical models) I don't think we'll have real rigor in economics.
In the meantime, we still have to do our best. People still want ways to predict the future which suffer less from human interference (which is ideally what a mathematical model will let you do). That's still better than just asking people what they think (in some ways).
A lot of simplifying assumptions have to be made to say anything useful about a system which includes billions of intelligent actors trading trillions of dollars. There's obviously room for improvement, and I think that'll happen once people are given the proper tools to make it happen.
We are almost to the point where an entity like Facebook or Amazon could do controlled economic experiments. Or they could gather so much data, that when filtering them based on the experimental criteria, whatever remains could show a significant result.
Aside from the technical possibility of doing economic experiments, there is also the ethics of doing them. You are not only involving humans, but doing so on a grand scale. To prove a point, you would not only need to possibly send an economy into a recession, but you would have to do so dozens of times to get significant results. The people you are experimenting upon might get a little murdery.
In the meantime, we still have to do our best. People still want ways to predict the future which suffer less from human interference (which is ideally what a mathematical model will let you do). That's still better than just asking people what they think (in some ways).
A lot of simplifying assumptions have to be made to say anything useful about a system which includes billions of intelligent actors trading trillions of dollars. There's obviously room for improvement, and I think that'll happen once people are given the proper tools to make it happen.