String theory often predicts the incorporation of a plentitude of ultralight scalars or axion like particles stemming from the topological complexity of the extra-dimensional spacetime manifold, defining the phenomenological landscape of the string axiverse. Randomised axiverse landscapes offer an inviting approach to probing the complexities of the axion field potentials in a self-consistent but ultimately simplified manner, approaching axion physics with the ideas of maximised entropy of the Lagrangian matrix space and canonical random matrix theory. Examples of this formalism include models of metastable vacua in supergravity for the superpotential Hessian, models of multi-field inflation and multi-component dark sector cosmology. The high-dimensional nature of effective theory formulated from considerations of the complete UV theory is often reduced by considering a series of simple yet very powerful nomothetic principles. From a four-dimensional effective theory perspective the universality of random matrix theory dictates priors on the axion parameter space in well aligned models take well known universal forms on logarithmic scales. We will briefly introduce a series of random matrix theory axiverse models based on axion field alignment and central limit theorems of free convoluted measure spaces for the canonical fields. We will also present an overview of an effective approach to the axion spectrum arising from the superpotential in the M-theory axiverse, using stochastic parameters of the model used to suitably stabilise the moduli. Such models are susceptible to test the viability of axion contributions to the cosmic history using hierarchical Bayesian inference models on simplified parameter spaces. In order to demonstrate how these models can be used to draw inferences on the axion parameter space, we will address astrophysical spin measurements of X-ray binary and supermassive black hole systems, which can exclude the existence of fields spanning a large portion of the ultralight bosonic mass parameter space, via the superradiance phenomenon. We will explore how these measurements are used to constrain properties of the universal statistical distributions in effective axiverse models, specifically the mass ranges and allowed numbers of fields present in the spectrum. Such a methodology generally excludes N ≥ 30 axion-like fields with a range of mass distribution widths and central values spanning many orders of magnitude, covering axion phenomenologies important to the dark sector of cosmology, grand unified theories and particularly for the recently imaged M87* , models of fuzzy dark matter.