A simple argument against the formation of singularities runs as follows:
1) Hawking radiation has a temperature T, proportional to 1/R where R is the radius of a black hole event horizon, but the horizon is not a real boundary, so the Hawking effect and effective temperature presumably continues to operate as one travels down towards the center of the hole.
2) The amount of energy produced by a black body at a given temperature is proportional to T**4 and exerts the same outward pressure on incoming particles as that which balances gravity in our sun.
3) If T is portional to 1/R and if the amount of energy produced is proportional to T**4, we will experience a repulsive force proportional to 1/R**4 which will eventually balance a gravitational pull that only increases at 1/R**2 and we will reach equilibrium. As incoming matter stops before reaching the hole center, no singularity ever forms.
This argument also provides cut-off-distance that allows gravity to be combined with ordinary quantum mechanics without encountering singularities.
Of course, it all hinges on the choice we made in (1) to use a formulation where T depends on 1/R, rather than depending on 1/M where M is the mass of the hole.
If this is the reason why it is invalid, it must be that the process which generates Hawking radiation at a particular spot on the radius of the event horizon is not dependent on the radius of curvature at that point, but on some other characteristic that distinguishes the hole at that point from one on another hole of different mass. If so, what property is this? If not, what exactly is the error in the above argument?