I second that. I see it as something to build intuition for "complex" problems. To make this more concrete: If you want to study the brain you can go the "biology" approach and describe neurons really well and build mathematical models for all the neuron types. Or you could do it the other way around with the "psychology" approach and put people/monkey/rats in an MRT. Both ways you learn important stuff but it will be hard to connect both worlds because simulation of enough neurons to predictive power over the outcome of an MRT is probably far fetched (although there are the human brain project or its US counterpart, the brain activity map project which attempt to do something like this). Complexity theory might help to learn how to close this gap. Things like synchronization (http://www.scholarpedia.org/article/Synchronization#Chaotic_...) or Self organized criticality (form the critical brain theory) could help distinguishing which parts of neuronal dynamics are due to biological restrictions and which form the function of the brain. With this knowledge one might be able to "dumb down" neuronal models enough to make large scale simulations without loosing to much of the processing dynamics. You might still not have predictive power then, but then again, complexity theory might help you to understand what the limitations of your approach are.

The same intuitions could be applied to other things. Large scale power grids are also often hard to predict when not moving into a sure fail state. Being able to analyze how you stabilize these systems without basically dumping a lot of money on them is the way to go (Looking in the past, the money will probably not be spend).

You could study the behavior of crowds and maybe make estimations on the safety large conventions build a "panic index" that calculates the risk of having something like at the Loveparade https://en.wikipedia.org/wiki/Love_Parade_disaster . Again - you would not be able to make a precise prediction of whats gonna happen but I'd say it'd even knowing if you have like a 0.5% Chance of a disaster would be worth knowing. (Of course, there are effective methods taught to prevent this disasters anyway. But sometimes you have new configurations that didn't occur in the past and you might catch these things with a simulation. I could be an additional approach)

Could you elaborate on the power grid idea? It seems like a good example of how to apply complexity theory to make hard decisions, in this case optimal investments in grid stabilization.

That's not really my strong side...

But a quick search brought this paper to the light which might serve as a starting point: https://res.mdpi.com/d_attachment/energies/energies-11-01381...

For example they report on a project where they used photovoltaic panels to stabilize changing power consumption in a power grids with minimal changes in the existing structure - something that is hard with traditional power plants since they basically have to much momentum for quick switching action. https://ieeexplore.ieee.org/document/7007647

Also, agent based simulations (building on the idea of self organized criticality) are a thing. With these setups you can test power grids on their reaction for certain failure types - something you don't want to test in real life. I assume these simulations would also be quite accurate since consumption and production should be well known, as well as the physical properties of transmission.