Without resorting to experiments, theories can be valuable in themselves, their soundness of argument, their coherence, and them not leading to confounding and condtradictory predictions can guide us as to their validity.

There is value in approaching problems analytically rather than resorting to empirical methods.

Modern psychology is heavily driven by both theory and empiric techniques. The theories themselves are rich and generally cohesive, but without empirical validation, they are essentially bare philosophy. Of course they aren't as water tight as the theories and observations of physics, but if you spend any time in the core psychological literature, you'll find a ton of theoretical work.

Spotted a mathematician. ;-)

> theories can be valuable in themselves

Maybe they can be (in pure mathematics, or philosophy, as the sibling comment points out), but not if your end-goal is to apply your theory or its predictions in the real world. Then suddenly the soundest and most coherent of theories can fall apart.

> There is value in approaching problems analytically rather than resorting to empirical methods.

Sure, but whether your arrive at your predictions analytically or empirically it does not preclude you from testing them experimentally.