Explanation:

The original sentence is erroneous.

Reason: The correct idiomatic expression is 'in the face of' and not with the facing of'.

In the face of (Idiom):

Meaning: Despite

E.g.: Reform had been introduced in the face of considerable opposition.

Hence ‘in the face of’ should be used in place of ‘with the facing of’ to make the sentence grammatically correct.

Among the given choices, only option C replaces the given bold part most appropriately.

The sentence after replacement becomes:

The RBI as a regulator has had qualified success in the face of structural impediments, including limited control over PSBs.

Option C is hence the correct answer.