No, Hybridization is not necessary for all chemical species. Most of the covalent bonds are having hybrid orbitals generally all the organic compounds.
But we represent hybridization in order to get the structure of molecule. for example- Though the orbitals of H or O don’t hybridize as in Carbon but still we need hybridization to show the geometry and shape.
Without hybridization, it would be difficult to predict the geometry of the species.