We study the pion-photon transition form factor (TFF) Fγ*γπ0 (Q2) using a state-of-the art implementation of light cone sum rules (LCSRs) within fixed-order QCD perturbation theory. The spectral density in the dispersion relation includes all currently known radiative corrections up to the next-to-next-to-leading-order (NNLO) and all twist contributions up to order six. Predictions for the TFF are obtained for various pion distribution amplitudes (DAs) of twist two, including two-loop evolution which accounts for heavy-quark mass thresholds. The influence of the main theoretical uncertainties is quantified in order to enable a more realistic comparison with the data. The characteristics of various pion DAs are analyzed in terms of the conformal coefficients a2 and a4 in comparison with the 1σ and 2σ error regions of the data and the most recent lattice constraints on a2 with NLO and NNLO accuracy. Our results provide more stringent bounds on the variation of the pion DA and illuminate the corresponding asymptotic behavior of the calculated TFF.