  Several attempts to detect extensive air showers (EAS) induced by
ultrahigh-energy cosmic rays have been conducted in the last decade based on
the molecular Bremsstrahlung radiation (MBR) at GHz frequencies from
quasi-elastic collisions of ionisation electrons left in the atmosphere after
the passage of the cascade of particles. These attempts have led to the
detection of a handful of signals only, all of them forward-directed along the
shower axis and hence suggestive of originating from geomagnetic and Askaryan
emissions extending into GHz frequencies close to the Cherenkov angle. In this
paper, the lack of detection of events is explained by the coherent suppression
of the MBR in frequency ranges below the collision rate due to the destructive
interferences impacting the emission amplitude of photons between the
successive collisions of the electrons. The spectral intensity at the ground
level is shown to be several orders of magnitude below the sensitivity of
experimental setups. In particular, the spectral intensity at 10~km from the
shower core for a vertical shower induced by a proton of $10^{17.5}$ eV is
7-to-8 orders of magnitude below the reference value anticipated from a scaling
law converting a laboratory measurement to EAS expectations. Consequently, the
MBR cannot be seen as the basis of a new detection technique of EAS for the
next decades.
