While I find asymptotic safety an intriguing idea, it would be disturbing for a truly fundamental model of gravity to have singularities.
Asymptotic Safety, Singularities, and Gravitational Collapse
Roberto Casadio, Stephen D.H. Hsu, Behrouz Mirza
Asymptotic safety (an ultraviolet fixed point with finite-dimensional critical surface) offers the possibility that a predictive theory of quantum gravity can be obtained from the quantization of classical general relativity. However, it is unclear what becomes of the singularities of classical general relativity, which, it is hoped, might be resolved by quantum effects. We study dust collapse with a running gravitational coupling and find that a future singularity can be avoided if the coupling becomes exactly zero at some finite energy scale. The singularity can also be avoided (pushed off to infinite proper time) if the coupling approaches zero sufficiently rapidly at high energies. However, the evolution deduced from perturbation theory still implies a singularity at finite proper time.
An Italian, an Iranian, and an American physicist walk into a bar ...