As I said, isolated black hole solutions are there to probe the UV end of General Relativity, rather than to act as practical astrophysical models. (We have those too, fwiw).

Hair or not there is _enormous_ entropy in black holes that have not yet evaporated. Since we are fairly sure that no physical black holes in our universe have evaporated or are likely to evaporate in the next 10^65 years (for the smallest extremely isolated unmerged stellar black holes), and black holes deep inside galaxies will be around much much longer, it is perfectly reasonable to ignore the outgoing radiation and say that black holes are _effectively_ bald until our eventually much bigger Hubble volume is much closer to de Sitter vacuum. Indeed, mergers of black holes in nature are expected to undergo rapid "balding" as their complicated dynamical modes decay. So I can't agree with your last paragraph.

It's relevant to consider the origin of the Hawking radiation. Differently accelerated observers looking at a region of a QM field that's in thermal equilibrium will disagree on particle count. The formation of a black hole horizon creates a dynamical spacetime in which there is an acceleration between past observers (before the horizon forms) and future observers; the future observer sees particles within a few Schwarzschild radiuses of the black hole that the past observer does not. We usually consider a photon field for simplicity, but the particle count difference applies to all matter fields generically.

These particles are effectively created by fossil curvature which classically puts them on complex geodesics that go to infinity. In departing the region near the black hole their contribution to the local energy-density drops, which dynamically shrinks the horizon area. That in turn reveals previously hidden fossil curvature (which runs all the way to the singularity), which again is equivalent to an acceleration between past observers (before the "shrink") and future ones (after the "shrink), with the latter seeing particles that the previous ones do not. Voilà: evaporation, provided that nothing replaces at least the energy density of the escaping Hawking radiation particles (since that increase the area of the horizon, hiding behind it some of the previously observable-outside-the-horizon fossil curvature and thus some of the dynamic production of particles).

The quantum picture is slightly different because the particles are extremely low energy, with wavelengths proportional to the curvature radius at the horizon. "Soft hair" makes sense when one realizes that the curvature at the horizon of supermassive black holes can be arbitrarily flat (i.e., you can in principle have particles with wavelengths as long as or longer than the Hubble length). That's a very different picture from fully classical pointlike particles. However it's not clear that that's sufficient to dent the enormous difference between the number of microstates inside the horizon and the eleven variables of the macrostate of a no-hair black hole.

Additionally, even if it did wipe out much of the black hole's entropy, there does not yet seem to be a way to unitarily evolve from pre-horizon state to fully evaporated state; the details of what exactly was in the black hole as the horizon formed and what drifted in later are not obviously encoded in "soft hair", and the assumption is that the encoding would involve strong gravity somehow (and it must as the horizon area gets small).

So even taking your idea of adding a bunch of additional macroscopic parameters to no hair's eleven (at a particular time coordinate), you still have a non-negligible fraction of a galaxy worth of mass inside the horizon of an SMBH that fits comfortably within Jupiter's orbit, and absent a quantum gravity theory you'll have little idea about how to count all the compatible microstates. The information loss you are blithely accepting in your second last paragraph is difficult to conceive: for a spherically symmetric black hole of merely one solar mass the horizon area is about 10^77 in Planck areas, which gives us the holographic entropy bound. 10^77 is greater than the value of S for all the gas, dust and noncompact stars in the Milky Way.

(Finally, I want to note that there are of course many approaches to the post-AMPS black hole information problem very different from Hawking et al.'s "soft hair"; however super- and ultramassive Schwarzschild black holes in dS vacuum are good model probes of each of these possible theories).