ABSTRACT Pulsar wind nebulae (PWNe) represent the largest class of sources that upcoming γ-ray surveys will detect. Therefore, accurate modelling of their global emission properties is one of the most urgent problems in high-energy astrophysics. Correctly characterizing these dominant objects is a needed step to allow γ-ray surveys to detect fainter sources, investigate the signatures of cosmic ray propagation, and estimate the diffuse emission in the Galaxy. In this paper, we present an observationally motivated construction of the Galactic PWNe population. We made use of a modified one-zone model to evolve for a long period of time the entire population. The model provides, for every source, at any age, a simplified description of the dynamical and spectral evolution. The long-term effects of the reverberation phase on the spectral evolution are described, for the first time, based on physically motivated prescriptions for the evolution of the nebular radius supported by numerical studies. This effort tries to solve one of the most critical aspects of one-zone modelling, namely the typical overcompression of the nebula during the reverberation phase, resulting in a strong modification of its spectral properties at all frequencies. We compare the emission properties of our synthetic PWNe population with the most updated catalogues of TeV Galactic sources. We find that the firmly identified and candidate PWNe sum up to about 50 per cent of the expected objects in this class above threshold for detection. Finally, we estimate that Cherenkov Telescope Array will increase the number of TeV-detected PWNe by a factor of ≳3.