I'll describe joint work with K. Iwaki relating the computation of free energies in the theory of topological recursion (TR) to the counting of "BPS states" (degenerate spectral networks) in 4d N=2 QFTs, in the case where the latter structure is "uncoupled". In particular, I'll describe a simple formula expressing the TR free energies as a sum over BPS states for the relevant quadratic differential and outline the proof, for examples arising from the hypergeometric spectral curve and its confluent degenerations. I will explain how this picture ought to generalize; if time permits, how Bridgeland's $tau$-function appears after taking the Borel sum. Based on arXiv:2010.05596.