We apply the semiclassical theory including the Berry curvature dipole, side jumps and skew scattering for a quantitative description of the circular photogalvanic effect (CPGE) in Weyl semimetals at intraband absorption. In contrast to gapped systems where they completely exhaust all contributions to the CPGE current, all previously known semiclassical mechanisms give a result different from that obtained using a complete quantum-mechanical approach. We show that this difference in the existing quasiclassical and full quantum-mechanical approaches persists at all spatial ranges of the disorder potential. Apparently, the implementation of another microscopic mechanism into the quasiclassical description of the CPGE is required.