Like you said, we can include gravity perturbatively in the framework of low-energy effective QFT, as reviewed in reference 1. This works because gravity is extremely weak at the energies that characterize modern particle-physics experiments. But the interest in quantum gravity revolves around nonperturbative/high-energy/strong-field issues, like the holographic principle and the informaion-loss paradox, both of which were already known in the 1970s (references 2,3,4) and were surely on Distler's mind in 1982.
Thanks to universality, very different theories can become indistinguishable from each other at sufficiently low resolution. Low-energy experiments can only fix the first several terms in the lagrangian on which perturbation theory is based. That's what allows us to include gravity in the Standard Model in the sense of low-energy effective theory (reference 1), and I'm guessing this was also the basis for Georgi's assertion. Terms of higher order in the cutoff are not resolved, so we cannot attack the interesting questions about quantum gravity — which are nonperturbative/high-energy/strong-field — by extrapolating upward from the low-energy effective theory.
Even if it was fair at the time, Georgi's "waste of time" judgement is obsolete now, because now we have approaches to studying quantum gravity that don't rely on extrapolating upward from a low-energy effective theory. Perturbative string theory is tightly constrained by numerous anomaly cancellation requirements, which are nonperturbative. Fully nonperturbative formulations like AdS/CFT are also available. (See references 5 and 6 for perspectives about the situation in the more realistic case of asymptotically de Sitter spacetime, which is not understood as well yet.) In hindsight, Georgi/Distler's statement
...there’s no decoupling regime in which quantum “pure gravity” effects are important, while other particle interactions can be neglected
seems to be true in an even stronger sense in string theory. Here's an excerpt from section 2.2 in reference 7:
Typically, the mass scale associated to [quantum gravity] physics is [the Planck mass] $M_p$, and one might expect that working at energy scales far below the Planck mass would mean that we lose sensitivity to such physics. But the conjecture says that if in the bulk of moduli space... the tower of states has a mass scale around the Planck mass $M_p$ ..., then at large field expectation values this mass scale is exponentially lower than $M_p$. Therefore, it claims that the naive application of decoupling in effective quantum field theory breaks down at an exponentially lower energy scale than expected whenever a field develops a large expectation value.
Whether this "stringy" phenomenon is our enemy or our friend, it at least corroborates the idea that the interesting questions about quantum gravity are not things we can study properly by decoupling it from everything else.
Donoghue (1995), Introduction to the Effective Field Theory Description of Gravity (https://arxiv.org/abs/gr-qc/9512024)
Bekenstein (1973), Black holes and entropy, Physical Review D 7, 2333-2346
Hawking (1975), Particle creation by black holes (https://projecteuclid.org/euclid.cmp/1103899181)
Hawking (1976), Breakdown of predictability in gravitational collapse, Phys. Rev. D 14, 2460–2473
Witten (2001), Quantum Gravity In De Sitter Space (https://arxiv.org/abs/hep-th/0106109)
Banks (2010), Supersymmetry Breaking and the Cosmological Constant (https://arxiv.org/abs/1402.0828)
Palti (2019), The Swampland: Introduction and Review (https://arxiv.org/abs/1903.06239)
