I've just realized I don't understand something pretty fundamental about the need to renormalize. Popular wisdom has it (or had it - forget the shift towards an effective framework) that theories that were not renormalizable had no predictive power, on account of the fact each n-point vertex function in such theories need to be renormalized anew, requiring new parameters to be measured at each n (see, e.g., Maggiore p139). But can't one say the following: say I am interested in studying only 2->2 interactions. Then presumably I only need to renormalize the 2, 3 and 4-point functions in order to derive predictions for these sorts of interactions. The infinitely many parameters apparently needed for a renormalizable theory (and once again, forget about EFTs) would only arise in the case that we study n->m particle relations in the limit that n & m go to infinity, which we never do. So why *were* renormalizable theories regarded as non-predictive? Any help much appreciated!