OWF by encrypting a constant?
Since $E$ is a secure PRP, instead of giving $C=E(X, S)$ to the adversary, you can give a uniform random $C\gets\mathcal{C}$.  To 'invert' this, adversary has to find a key $X'$ such that $E(X', S)=C$.

So, the construction being one-way function is equivalent to the property that, given a uniform random $C$, it should be hard to find $X$ such that $E(X, S)=C$.  I don't think that this necessarily follows from $E$ being secure, strong PRP.  For example, when the block cipher has polynomial-sized small domain (rather unusual case, I know), then this would not hold.  On the other hand, most reasonable block cipher constructions would have this property, I guess.  So, I think it could be considered as a secure OWF for practical purposes, in reasonable settings.