But, given you've given a whole spiel about about EFTs, you can think of the lattice formulation of QCD as an EFT whose cutoff is the lattice spacing. We can compute the mass of hadrons and take the continuum limit / cutoff to infinity. And when we take that limit holding some physical hadronic observables fixed, the spectrum matches perfectly. So I think it's relatively unfair and misleading to say that because we can't do it with pen and paper we can't make any low-energy QCD predictions at all whatsoever.
What always drives me crazy about stories like the OP is that strongly coupled theories are automatically technically natural. But most phenomenologists don't like them because they, not being proficient supercomputer programmers, can't calculate anything.