We report a combined experimental and theoretical investigation that reveals a new mechanism responsible for the enhancement of electron-phonon coupling in doped semiconductors in which multiple inequivalent valleys are simultaneously populated. Using Raman spectroscopy on ionic-liquid-gated monolayer and bilayer MoS2, WS2, and WSe2 over a wide range of electron and hole densities, we find that phonons with a dominant out-of-plane character exhibit strong softening upon electron accumulation while remaining unaffected upon hole doping. This unexpected-but very pronounced-electron-hole asymmetry is systematically observed in all monolayers and bilayers. By performing first-principles simulations, we show that the phonon softening occurs when multiple inequivalent valleys are populated simultaneously. Accordingly, the observed electron-hole asymmetry originates from the much larger energy separation between valleys in the valence bands-as compared to the conduction band-that prevents the population of multiple valleys upon hole accumulation. We infer that the enhancement of the electron-phonon coupling occurs because the population of multiple valleys acts to strongly reduce the efficiency of electrostatic screening for those phonon modes that cause the energy of the inequivalent valleys to oscillate out of phase. This robust mechanism is likely to play an important role in several physical phenomena, possibly including the occurrence of superconductivity in different transition metal dichalcogenides.