Growing Inventory of Black Holes Offers a Radical Probe of the Cosmos

You are conflating new physics with new experiments testing the limits of established physics.

New physics is the requirement for explanations of observations which cannot accord with or be derived from existing fundamental theory. In the case of merger chirps detected at LIGO, Virgo, and other detectors, that's General Relativity. New physics would be chirps that [a] are traceable to a compact-object merger event through other observations (direct emissions of various types of radiation, and their echoes) but [b] have a chirp waveform that contradicts "balding" (deformations of the event horizons raised by each pair-member on the other should disappear in on the order of horizon light-crossing time) or flavours of equivalence principle (e.g., the universality of free fall shapes the chirp).

Nobody working in high energy astrophysics seriously doubts the existence of astrophysical black holes, nor that they are extremely well-modelled by small perturbations of a handful of simple metrics (General Relativity being a metric theory of gravitation). There are plenty of arguments about the details of the perturbations and about whether General Relativity itself can be derived from some more fundamental theory, but those arguments are confronted with quite a bit of observational data that completely support General Relativity and offer no support for practically any proposal which reduces to (or produces) General Relativity in the centres of active galaxies.

Furthermore, there is plenty of evidence for the mergers of galaxies, and nothing (in General Relativity) forbidding the merger of such galaxies' central black holes. Nobody should seriously dispute the merger of supermassive black holes, even if the "final parsec" mechanisms that allow for quicker mergers (i.e., billions of years -- less than the age of the universe, in particular -- rather than trillions of years) are not yet strongly understood.

> The actual singularity physics

are unobserved. Searches for primordial BH evaporation remnants and naked singularities will continue -- you automatically get the latter searches in chirp analysis and multimessenger matching -- and you'd have evidence for new physics if there is any evidence for such things, because they are not allowed by General Relativity.

Astrophysically, black holes are characterized by the properties of their event horizons, not the properties of their singularities (even theoretically it's the exterior metric that counts; nobody, especially not Kerr himself, thinks the interior BH metric is generally a good physical description). As long as it stays enshrouded by a horizon (thus protecting the exterior metric tensor and some energy conditions), the matter that has fallen in can be in any sort of arrangement inside the horizon, including but far from limited to a classical singularity. Post Ken Wilson (renormalization and effective field theory), we should be agnostic about such things.

> indirect observations of [black hole] properties

The chirp mass is a physical property of the black hole pair that is directly measured by gravitational wave detectors, comparable to how the reduced mass is a directly measurable attribute of pairs of non-relativistic celestial objects (and cf. linearized gravity). Chirp masses are verifiable by studying the orbits of stars and molecular clouds around or past the merging pair.