[tjradcliffe]

Your first point is correct: the relationship between black holes and the initial state of the universe is not clear. Whether or not there was a primordial singularity or something else is an open question.

With regard to the question "If not black holes, then what?", this is a problem. There is a strict upper limit on neutron stars of about 1.4 solar masses. Beyond this, gravity is stronger than the repulsive core of the strong nuclear force, and the star should collapse. If the process described in this paper is what actually occurs, the star will shed mass due to Hawking radiation while collapsing. The end-state of that process must be either a neutron star (which can't have more than 1.4 solar masses) or something else. There doesn't seem to be any "something else" in the offing, which makes that million-solar-mass thing in the centre of our galaxy deeply mysterious.

A new theory that makes an old "settled" phenomenon mysterious is not all that uncommon in the sciences, so it's reasonable to take a wait-and-see attitude toward this idea, but I'm not enormously hopeful that it'll pan out very well in the long run.

[squozzer]

So it seems a cycle of collapse and Hawking radiation will occur until the star no longer has enough mass to collapse.