We present a Regge model for pion photoproduction which is basically free of parameters within the framework of the $s$-channel helicity amplitude. For completeness we take into account axial mesons ${a}_{1}(1260)$, ${b}_{1}(1235)$ and tensor meson ${a}_{2}(1320)$ in addition to the primary $\ensuremath{\pi}+\ensuremath{\rho}$ exchanges for charged pion photoproduction, while the axial meson ${h}_{1}(1170)$ exchange is added to the model of $\ensuremath{\omega}+{\ensuremath{\rho}}^{0}+{b}_{1}$ exchanges for the neutral case. The present model deals for the first time with the ${a}_{2}$ and ${h}_{1}$ Regge poles in the $s$-channel helicity amplitude. For model independence, we use coupling constants of all exchanged mesons determined from empirical decay widths or from the SU(3) relations together with consistency check with existing estimates that are widely accepted in other reaction processes. Based on these coupling constants the simultaneous description of four photoproduction channels is given. Within the Regge regime, $s\ensuremath{\gg}4{M}^{2}$ and $\ensuremath{-}t<2$ GeV${}^{2}$, cross sections and spin polarization asymmetries at various photon energies are analyzed and results are obtained in better agreement with experimental data without referring to any fitting procedure. The model confirms dominance of the nucleon Born term in the sharp rise of the charged pion cross section at very forward angles, while dominance of the $\ensuremath{\omega}$ exchange with the nonsense wrong signature zero leads to the deep dip in the neutral pion cross section. In contrast to existing models, however, our model for the charged pion case shows quite a different production mechanism due to the crucial role of the tensor meson ${a}_{2}$ exchange in the cross section and spin polarization asymmetries. Also the axial meson ${b}_{1}$ exchange is found to give a sizable contribution to the photon polarization asymmetry. In the neutral case, the role of the ${b}_{1}$ is not significant, but the isoscalar ${h}_{1}$ exchange gives an important contribution to the dip-generating mechanism in the photon polarization, showing the isoscalar nature of the process with the $\ensuremath{\omega}$. These findings demonstrate validity of the present model with the prompt use of the tensor meson ${a}_{2}$ and axial meson ${h}_{1}$ for a wider application.