ABSTRACT We present a systematic study of X-ray cavities using archival Chandra observations of nearby galaxy clusters selected by their Sunyaev–Zel’dovich (SZ) signature in the Planck survey, which provides a nearly unbiased mass-selected sample to explore the entire AGN feedback duty cycle. Based on X-ray image analysis, we report that 30 of the 164 clusters show X-ray cavities, which corresponds to a detection fraction of 18 per cent. After correcting for spatial resolution to match the high-$\mathit{ z}$ SPT-SZ sample, the detection fraction decreases to 9 per cent, consistent with the high-z sample, hinting that the AGN feedback has not evolved across almost 8 Gyrs. Our finding agrees with the lack of evolution of cool-core clusters fraction. We calculate the cavity power, Pcav, and find that most systems of our sample have enough AGN heating to offset the radiative losses of the intracluster medium.