Could nature be simpler than what we want it to be? Newton's law of universal gravitation is a 2-body problem (though a mass disparity of very large and very small). Coulomb's law of electrostatic force is also a 2-body problem of electric charges.
But the n-body problem is solved using statistical mechanics which necessarily incorporate the theory of probability and random variables. Anything more than 3 bodies, probability is involved and the process becomes stochastic instead of deterministic. But when n is just a little bit greater than 2, perturbation theory can be used. In astrodynamics, the n-body problem is solved by taking the interaction of 2 bodies at a time and then add all the 2-body interactions together.