What Brandon said (notably by adding "even if Rand is now sane" suggests consequences for Rand. What you bring up isn't really "consequences", it's repercussions on the plot in general for the fact Rand used the TP. Those may be there too (the epiphany itself is more likely to force Moridin to change his strategy, if you ask me), but Brandon seemed to talk about consequences for Rand or through Rand (his "dark aura" may not go away so easily, for example).

A distinct possible consequence, now that Rand has destroyed the CK, is that the amount of saidin he could get from the CK helped him keep the desire to use the TP again at bay. Now, if Rand finds himself in a dark spot or a position of weakness, he might struggle a lot more resisting the temptation to embrace the TP (which gave him a feeling of utter power similar to a far greater amount of saiding that Rand can embrace unaided... the sort of feeling he could reproduce by drawing on the CK and now could only be embracing the TP). Demandred (or Moghedien) experienced something similar - they used the TP only when it was their last chance/last hope (it's not totally unlike how Nynaeve broke her block, except in her despair/darkness she gave up, and this surrender was what she needed. Previously, she could embrace saidar only when she was so blinded by anger she forgot she was surrendering to saidar).