We present a thorough observational investigation of the heuristic quantised ringdown model presented in Foit & Kleban (2019). This model is based on the Bekenstein-Mukhanov conjecture, stating that the area of a black hole horizon is an integer multiple of the Planck area $l_P^2$ multiplied by a phenomenological constant, $alpha$, which can be viewed as an additional black hole intrinsic parameter. Our approach is based on a time-domain analysis of the gravitational wave signals produced by the ringdown phase of binary black hole mergers detected by the LIGO and Virgo collaboration. Employing a full Bayesian formalism and taking into account the complete correlation structure among the black hole parameters, we show that the value of $alpha$ cannot be constrained using only GW150914, in contrast to what was suggested in Foit & Kleban (2019). We proceed to repeat the same analysis on the new gravitational wave events detected by the LIGO and Virgo Collaboration up to 1 October 2019, obtaining a combined-event measure equal to $alpha = 15.6^{+20.5}_{-13.3}$ and a combined log odds ratio of $0.1 pm 0.6$, implying that current data are not informative enough to favour or discard this model against general relativity. We then show that using a population of $mathcal{O}(20)$ GW150914-like simulated events - detected by the current infrastructure of ground-based detectors at their design sensitivity - it is possible to confidently falsify the quantised model or prove its validity, in which case probing $alpha$ at the few % level. Finally we classify the stealth biases that may show up in a population study.
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