Why wouldn't summing all possibilities be the simpler solution?

Thing about Monte Carlo simulations - it's simpler to just try all possibilities than to figure out what is the formula of the correct result.

Neural networks also work like that - you randomly do things and propagate errors with simple rules instead of figuring out the complex formula that would give you the answer.

There seems to be a lot of power in summing up all the things.

If our universe is a computation, our practical experience seems to suggest that a Monte Carlo like simulation of it would be more efficient than a closed-form formula.