> But we don't have empirical evidence of black holes - we have circumstantial evidence of very dense blobs - they could be neutron stars or other things.
We have images of stars rotating around some very dense invisible stuff. Too dense to be supported by neutron degeneracy. What more do you want? We can't exactly get pictures of the interior.
We do not have pictures of stars rotating around dense stuff. All the pictures of galaxies could be stars rotating around each other. Add in dark matter and you really have no idea what they are rotating around.
What we do have is pictures of gravitational lensing, and jets, and some other evidence, but certainly not stars rotating around dense stuff. And you are quite overestimating our ability to measure the size of the object - it could be very dense, but large, so not a black hole, but something else.
You quite missed the point - the whole point was that loop quantum gravity says that you can not get infinity dense, so even if neutron degeneracy can not hold it up, the loop quantum degeneracy will.
Perhaps quark degeneracy exists?
There is no evidence that black holes (as infinitely dense singularities) exists. There is only evidence of very big things, and our current theories don't know what else it could be. But that is NOT the same as evidence of a black hole.
We have images of stars rotating around some very dense invisible stuff. Too dense to be supported by neutron degeneracy. What more do you want? We can't exactly get pictures of the interior.