The very existence of more than a dozen of high-redshift (z ≳ 4) blazars indicates that a much larger population of misaligned powerful jetted active galactic nucleus (AGN) was already in place when the Universe was ≲1.5 Gyr old. Such parent population proved to be very elusive, and escaped direct detection in radio surveys so far. High-redshift blazars themselves seem to be failing in producing extended radio lobes, raising questions about the connection between such class and the vaster population of radio galaxies. We show that the interaction of the jet electrons with the intense cosmic microwave background (CMB) radiation explains the lack of extended radio emission in high-redshift blazars and in their parent population, helping to explain the apparently missing misaligned counterparts of high-redshift blazars. On the other hand, the emission from the more compact and more magnetized hotspots are less affected by the enhanced CMB energy density. By modelling the spectral energy distribution of blazar lobes and hotspots, we find that most of them should be detectable by low-frequency deep radio observations, e.g. by LOw-Frequency ARray for radio astronomy and by relatively deep X-ray observations with good angular resolution, e.g. by the Chandra satellite. At high redshifts, the emission of a misaligned relativistic jet, being debeamed, is missed by current large sky area surveys. The isotropic flux produced in the hotspots can be below ∼1 mJy and the isotropic lobe radio emission is quenched by the CMB cooling. Consequently, even sources with very powerful jets can go undetected in current radio surveys, and misclassified as radio-quiet AGNs.