Context. The Universe's assumed homogeneity and isotropy is known as the cosmological principle. It is one of the assumptions that led to the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric and is a cornerstone of modern cosmology, because the metric plays a crucial role in the determination of the cosmological observables. Thus, it is of paramount importance to question this principle and perform observational tests that may falsify it. Aims. Here, we explore the use of galaxy cluster counts as a probe of a large-scale inhomogeneity, which is a novel approach to the study of inhomogeneous models, and we determine the precision with which future galaxy cluster surveys will be able to test the cosmological principle. Methods. We present forecast constraints on the inhomogeneous Lemaitre-Tolman-Bondi (LTB) model with a cosmological constant and cold dark matter, basically a Lambda CDM model endowed with a spherical, large-scale inhomogeneity, from a combination of simulated data according to a compilation of 'Stage-IV' galaxy surveys. For that, we followed a methodology that involves the use of a mass function correction from numerical N-body simulations of an LTB cosmology. Results. When considering the Lambda CDM fiducial model as a baseline for constructing our mock catalogs, we find that our combination of the forthcoming cluster surveys will improve the constraints on the cosmological principle parameters and the FLRW parameters by about 50% with respect to previous similar forecasts performed using geometrical and linear growth of structure probes, with +/- 20% of variations depending on the level of knowledge of systematic effects. Conclusions. These results indicate that galaxy cluster abundances are sensitive probes of inhomogeneity and that next-generation galaxy cluster surveys will thoroughly test homogeneity at cosmological scales, tightening the constraints on possible violations of the cosmological principle in the framework of Lambda LTB scenarios.