Gamma-ray luminosities of some quasar-associated blazars imply jet powers reaching values comparable to the accretion power even if assuming very strong Doppler boosting and very high efficiency of gamma-ray production. With much lower radiative efficiencies of protons than of electrons, and the recent reports of very strong coupling of electrons with shock-heated protons indicated by Particle-in-Cell (PIC) simulations, the leptonic models seem to be strongly favored over the hadronic ones. However, the electron-proton coupling combined with the ERC (External-Radiation-Compton) models of gamma-ray production in leptonic models predict extremely hard X-ray spectra, with energy indices about 0. This is inconsistent with the observed 2-10 keV slopes of blazars, which cluster around an index value of 0.6. This problem can be resolved by assuming that electrons can be cooled down radiatively to non-relativistic energies, or that blazar spectra are entirely dominated by the SSC (Synchrotron-Self Compton) component up to at least 10 keV. Here, we show that the required cooling can be sufficiently efficient only at distances r