I must admit it is a few years since the days of my Hawking cosmology obsession, however:
Matter-antimatter pairs spontaneously form and dissipate on a quantum level throughout the universe. As I remember it, Hawking radiation is merely the process of one of the two particles of the matter-antimatter pair falling into the event horizon on pairs that formed close to a black hole, leaving a "radiation" of particles that do not dissipate in the formation-dissipation cycle.
If this is truly the mechanism of Hawking radiation, I fail to see how you can arrive at your last paragraph ("which means that the hypothetical perfect singularity black hole model, which can only absorb matter, does not exist.").
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I must admit it is a few years since the days of my Hawking cosmology obsession, however:
Matter-antimatter pairs spontaneously form and dissipate on a quantum level throughout the universe. As I remember it, Hawking radiation is merely the process of one of the two particles of the matter-antimatter pair falling into the event horizon on pairs that formed close to a black hole, leaving a "radiation" of particles that do not dissipate in the formation-dissipation cycle.
If this is truly the mechanism of Hawking radiation, I fail to see how you can arrive at your last paragraph ("which means that the hypothetical perfect singularity black hole model, which can only absorb matter, does not exist.").