Is it really that strange that random matrix theory models so many things though? Matrices without stochasticity can already model so many things in nature. And the reason for that is much more because they are a really well studied area of math, rather than because of some deep mysterious thing about nature. (It's much more about that being the conventional tool that physicists learn in school.) Take some really well used technique (matrix theory) and add another property (randomness) and is it really that strange that the result (random matrix theory) explains a larger set of phenomenon than what was explained by each piece individually?
Matrices don't have to be "some deep mysterious thing about nature" to be important in themselves and not just beause they are well-studied. They merely need to be deep.
"Matrices" is just a word for "Linear operators over finite-dimensioned spaces". Linear stuff is important. Finite dimensional systems are imporant. And even infinite dimensional linear systems tend to have the same properties as finite dimensional ones. All of this makes matricies important in their own right.
This made me think of the Central Limit Theorem. (If 'non-contrived' independent observations with random variability are summed and normalized, they end up exhibiting the standard Gaussian "bell curve".) All kinds of natural "real world" phenomena end up neatly obeying a function that seems odd:
f(x) = K / sqrt(exp(x*x))
(The above characterization assumes N(0,1), and re-arranges terms a slight amount to highlight the interesting nature of the function.)
If you study the so-called level spacing of a Hamiltonian with disorder drawn from a uniform random distribution, you will recover a Poisson distribution. As you turn down the disorder, you will reproduce the statistics the Czechs discovered in the bus system.
