Parshas Parah is the outlier of the four special parshios read in the 6 weeks before Pesach. There is no reason why purification is more relevant before Pesach than it is before Shavuos or Succos. Yet we only make a point of emphasizing the need to be pure on Pesach.
There must be a broader concept that is being addressed. I think the extensive piyutim, extra poems (that most shuls no longer say) address the super-rational element of the mitzvah, that seems to violate the rules of logic. (Purifies the impure, and defiles the pure.)
This idea has to be part of the foundation of our relationship with the Almighty; Especially at Pesachtime, when all the mitzvos seem to be commemorative, and make sense on a symbolic level. And the 26 haggados I have explain how logical and sensible every line and mitzvah and custom is. Yet as we relive our birth as a nation, we need to “get” the concept that we are about to be betrothed to a Groom who won’t always make sense to us.