https://arxiv.org/abs/1911.02967John F. Donoghue
(Submitted on 7 Nov 2019)
The present practice of Asymptotic Safety in gravity is in conflict with explicit calculations in low energy quantum gravity. This raises the question of whether the present practice meets the Weinberg condition for Asymptotic Safety. I argue, with examples, that the running of Λ and G found in Asymptotic Safety are not realized in the real world, with reasons which are relatively simple to understand. A comparison/contrast with quadratic gravity is also given, which suggests a few obstacles that must be overcome before the Lorentzian version of the theory is well behaved. I make a suggestion on how a Lorentzian version of Asymptotic Safety could potentially solve these problems.
I have not read this paper yet, but Lubos Motl blogs about it here: "A serious critique of the real-world Asymptotic Safety program for quantum gravity".
The points I would list in favor of asymptotic safety's significance and viability, may be found in this Physics Stack Exchange question-and-answer: the prediction of the Higgs boson mass, successfully dealing with the Goroff-Sagnotti two-loop counterterm, and a recent paper exploring asymptotic safety as a Planck-scale regime between field theory and string theory.