While The Interpretation of the Bible in the Church commends diachronic study as "indispensable," the Pontifical Biblical Commission does recognize the limits of source criticism. Here's what the document has to say on the matter:
In the desire to establish the chronology of the biblical texts, this kind of literary criticism restricted itself to the task of dissecting and dismantling the text in order to identify the various sources. It did not pay sufficient attention to the final form of the biblical text and to the message which it conveyed in the state in which it actually exists (the contribution of editors was not held in high regard). This meant that historical-critical exegesis could often seem to be something which simply dissolved and destroyed the text. This was all the more the case when, under the influence of the comparative history of religions, such as it then was, or on the basis of certain philosophical ideas, some exegetes expressed highly negative judgments against the Bible.