I've suggested in previous posts at this blog that the lack of CP violation in the electromagnetic and strong forces may be fundamentally due to the fact that their force carrying bosons, the photon and the gluon respectively, have no mass and therefore travel in a vacuum at the speed of light, in which they do not experience time and hence should not experience an arrow of time.
Neutrinos have mass, but in practice, the mass is so low that neutrinos of any decent energy travel at something extremely close to the speed of light and hence experience the passage of time very, very slowly. This implies, if my hypothesis is correct, that the CP violating phase in the PMNS matrix ought to be very, very small in magnitude, probably to the point of being non-observable. The lack of charge in neutrinos also means that any CP violation is indistinguishable from a P violation by itself or a T violation by itself.
Also, if QCD lattice computations are correct in concluding that gluons have a momentum dependent mass in the infrared, then even though high energy QCD may not be CP violating at an observable level, there might be CP violation in low energy QCD that is extremely hard to observe due to quark confinement.
An approximation of the PMNS matrix as lacking a CP violating phase entirely, whether or not it is truly exact, therefore, may be very servicable. This, in turn, would mean that the matrix should be capable of being approximated accurately with three rather than four parameters, and if the real theta angles in the PMNS and CKM matrixes respectively form unitary triangles, then you can actually describe the CKM matrix with three parameters (two of three thetas and a CP violating phase) and the PMNS matrix with two (two of three theata and no CP violating phase). Assuming that quark-lepton complementarity is accurate, moreover, both of the PMNS matrix parameters can be precisely determined from the three CKM matrix parameters alone. Thus, a theoretically possible eight parameters in the PMNS and CKM matrixes may actually be describable with just three parameters due to the interrelationships of the matrixes.
The even bigger step is that there is good reason to think that the mass ratios of the fermions may have a functional relationship to the elements of the CKM and PMNS matrixes, which would suggest that one could describe the 12 fermion mass parameters and 8 CKM/PMNS matrix parameters in the Standard Model with just four parameters (two of three CKM theta angles, one CP violation phase in the CKM matrix, and one mass parameter from which the others are derived; the W/Z boson masses can be derived from these other parameters). Of course, since the functions are related to each other that are multiple possible parameterizations with that many degrees of freedom. Still, eliminating 11 experimentally determined fermion mass parameters and five CKM/PMNS parameters from the Standard Model, if it could be accomplished, would be a profound leap and would have the practical effect of making it possible to use theory to exactly determine parameters that have to be estimated only roughly right now. This is particularly an issue in QCD because the lighter quark mass estimates are very rough and this leaves QCD with a far less solid foundation upon which to do calculations with the equations that have so far proved to be accurate.
One also needs three coupling constants in the Standard Model (for the electromagnetic, strong and weak forces), bringing you to seven parameters that must be experimentally fitted, and one probably needs to have at least one experimental fit parameter for each of the beta functions for the running of those coupling constants, although fundamental explanations for those functions have been suggested.
On the other hand, truly exteme CP violation in neutrinos, which is hard to detect due to lack of charge, could look like non-CP violation, but could perhaps lead to superluminal outcomes.