This seems to me to be moving the goalposts, and additionally to put a lot of work into that word 'simple'. Suppose the symmetry was CPXYZT instead, would required the CPXYZ transformation still be simple? Is there a criterion for deciding other than "Sean Carroll thinks so"?
I agree that this definition is fuzzy. (So does Carroll, as he makes clear in the text immediately following the bit I quoted.) But no, I don't think it's moving the goalposts, though it may not be putting them where you would prefer them to be.
I take the basic arrow-of-time problem to be something like this: The universe appears to be dramatically asymmetric in time: it is expanding in one time direction and contracting in the other; if we trace its evolution in the direction we call "past" according to our best understanding of the physics, we ...