A major obstacle for computing optical spectra of solids is the lack of reliable approximations for capturing excitonic effects within time-dependent density functional theory. We show that the accurate prediction of strongly bound electron-hole pairs within this framework using simple approximations is still a challenge and that available promising results have to be revisited. Deriving a set of analytical formulas we analyze and explain the difficulties. We deduce an alternative approximation from an iterative scheme guided by previously available knowledge, significantly improving the description of exciton binding energies. Finally, we show how one can "read" exciton binding energies from spectra determined in the random phase approximation, without any further calculation.