Can a unified physics theory have a smaller number of couplings than its effective field theory? Suppose that we have a QFT that has $n$ number of physical coupling constants, or there are $n$ coupling constants required to perturbatively renormalize the given QFT.
Suppose this QFT to be an effective field theory of some unification theory. Is it possible that this unification theory has number of coupling constants less than the given QFT?
That is, can some number of coupling constants be artifacts of us trying to look at IR physics, and not fundamental to be absorbed by more fundamental coupling constants?
This question is asked because, in renormalization, we usually talk of some coupling constants of a hypothetical unifying theory vanishing as we lower our energy scale to the scale of the given effective field theory. In this view, it seems as if we think of this hypothetical unifying theory as having a larger number of coupling constants than the effective field theory. But is this because we want to more conveniently look at IR physics, and not because the number of coupling constants has any fundamental significance?
 A: There are definitely some ways in which one can have a UV theory with fewer coupling constants than in the IR description. For this to be the case, one needs a mechanism in which the large  number of coupling constants at low energy is generated by some mechanism that is not directly visible in the IR theory. 
A simple example would be a UV theory of which the Lagrangian would be something else than a polynomial in the fields. One could expand this Lagrangian as a power series, suddenly having a large  number of coupling constants, corresponding to the coefficients of the expansion. 
It is also possible that the UV theory has an entirely different structure than the IR quantum field theory. This is obviously the case in string theory, in which there is only one fundamental constant, the string scale $\alpha '$. However, string theory is supposed to yield the Standard Model (with all its seemingly arbitrary couplings and masses) as a low-energy description. Admittedly, string theory does contain the additional arbitrariness of choosing a compactification manifold, but there might be dynamical mechanisms within the theory by which this choice is fixed in some way. 
