Prompt emissions from TeV blazars pair produce off the extragalactic background light and the highly energetic resulting pair beams then cascade through inverse Compton scattering to give rise to secondary gamma-rays. Such reprocessed cascade emission that can be associated with individual blazar sources has not been detected thus far. The absence of pair halos around these sources along with the non-observation of isotropic gamma-ray background excess, seems to suggest that collective plasma effects, such as beam-plasma instabilities can play a crucial role in alleviating this GeV-TeV tension by transferring the energy from the pair beams into the background plasma of the intergalactic medium (IGM). This has profound implications not only for TeV astrophysics, but also the strength of the intergalactic magnetic field and properties of dark matter (DM). A direct consequence of the instability losses and IGM heating is the modification of thermal history at late times, which suppresses structure formation particularly in baryonically underdense regions, potentially holding a clue towards resolving the small-scale crisis in cosmology. In a blazar-heated universe, the observation of dwarf galaxies and Lyman-$\alpha$ measurements present a favoured mass range for DM candidates such as light axion-like particles.