The debate that seems to be happening right now is what does it mean that '... the formation of the black hole does not create nor destroy entropy, so the black hole must contain zero or nearly zero entropy as well.' This is correct, of course, except that the material we observe with zero or nearly zero entropy is 'Bose-Einstein condensate' (BEC) and BEC brings properties to the event horizon (such as non-compressibility), and indeed to the process of gravitational collapse, that have not previously factored into black-hole theory or yet been addressed.
Pawel O. Mazur and Emil Mottola's seminal paper have tried to address this, but their results are somewhat controversial. [Gravitational Condensate Stars: An Alternative to Black Holes] They found that as a star collapses, in-falling matter sheds its entropy becoming Bose-Einstein condensate (BEC) which imposes constraints on what can and cannot happen at the even-horizon. Some of these constraint exclude necessary conditions for the formation of traditional black-holes (such as the formation of a singularity, infinite space-time curvature, etc.). Their object, though not quite a 'black-hole', will look, act, and feel very similar (tis said), but will instead be a gravitational vacuum condensate star with event-horizon (consisting of BEC), but no singularity. Actually the interior is described to be a segment of de Sitter space.
This solves Hawking's Black-Hole information paradox because rather than having in-falling matter transforming into a pure quantum states completely independent of Hawking-Radiation destroying information about the original quantum state, it is suggested that instead what happens is that all in-falling matter (protons, neutrons, electrons, etc...) transforms instead into a quantum state known as “super-atom” (coherence). No information is lost since Hawking-Radiation is a product of this transformation, not independent of it.
The appeal of this theory is that it provides a much clearer understanding of behaviour at the event-horizon boundary and solves many stability problems. Some of its consequences are also testable [Hawking radiation in a two-component Bose-Einstein condensate (BEC). P.-É. Larré and N. Pavloff]. Furthermore, this theory solves Hawking's 'Black-Hole Information paradox' by establishing the basis for thermodynamic stability. The Gravastar is theorized to have very low amounts of entropy, in contrast with black holes which apparently have a billion times more entropy than the dying star that formed it.
This theory, as original posed, had sight problems with it, but Matt Visser and David Wiltshire were able to solve them by posing a slight variation [Stable Gravastars — an alternative to black holes?] which also provide an alternate explanation for gamma ray bursts. Even with all of this, there is criticism. The problem that still remains is about the creation of a Gravastar; is a collapsing star capable of shedding enough entropy upon implosion to cause a change in quantum state to 'super-atom'? If "yes", Gravastars and Black-holes would appear the same observationally, and produce similar signatures. (Actually I question this since BECs exhibit the ability to significantly slow the speed of light to a crawl. The only question I've asked is whether or not this is completely true. "Are Black-holes and Gravastars observationally identical? No one has yet answered.)
With respect to your question about 'hair', if this theory holds, can such a cold condensate body, a super-atom, indeed have angular momentum or electric charge? In fact the Gravastar is very close to the ideas of Kerr as rotating Black Hole yet solves the 'hair problem' by positing that the super-atom would modulo quantum fluctuations (Kerr/Hairless hybrid?). Can there be magnetic fields in de Sitter space? Pawel Jan Morawiec says 'Yes, no problem!'. He argues that in the Gravastar model, the non-vanishing magnetic field could be present in de Sitter space (by studying massless Dirac fields as an example of a matter field in the de Sitter spacetime in the vicinity of an event horizon), this postulated to be related to the Josephson effect [Physical and geometrical aspects of de sitter interior of a Gravastar].
It's a fascinating theory, but we'll likely have to wait for the jury to weigh in ...
[Cosmological milestones and Gravastars — topics in General Relativity, Céline Cattën (supervised by Matt Visser)]
[Scattering of atoms on a Bose-Einstein condensate, Uffe V. Poulsen, Klaus Molmer] - where an atomic wavepacket seemingly leaves the condensate before its arrives