In QFT Vol2 written by Weinberg(Chap 16-17), or very much similarly in Adel Bilal's notes(Chap 7), a powerful way of proving renormalizability is presented: Analyze the symmetries of the quantum effective action (QEA), and since QEA generates all 1-particle irreducible diagrams, the symmetry of it tells us what kind of counterterms are needed. If the symmetry is strong enough to limit the form of counterterms such that they are already contained in the original Lagrangian, the renormalizability is proved.
But it seems that, for the terms in their intermediate derivations to make sense at all, they must be understood as already regularized. However, it is not obvious that there exists a regularization scheme that respects all the utilized symmetries(In the QCD case they are Lorentz invariance, global gauge invariance, antighost translation invariance, ghost number conservation). Is this a missing step in their proof?