I would not agree that there are “many interpolations.”  I would say that there are somewhere around a dozen or so examples where there have been significant interpolations into the New Testament text.  However, in nearly every case, the fact that an interpolation has occurred, for whatever reason, is easily detectable by biblical scholars because of the thousands of ancient manuscripts we have, including manuscripts from before the time many of these interpolations occurred.  In other words, despite the fact that a biblical scribe inserted a word or comment into a text, whether accidentally or on purpose, the interpolation has no effect on the biblical text because we are aware of it, can note it, and can produce a translation which does not include the addition.

As to your question, God had two choices, if you will.  He could have intervened and forced the hand of all copyists so as to steal their free will and to supernaturally inspire all copying of the Bible, or he could have allowed fallible humans copy the Scriptures.  Clearly, God decided not to supernaturally intervene with all the thousands of examples of people copying the texts of the New and Old Testament.  He chose to use fallible humans.  In this case, God was not conceding his sovereignty, but he was choosing to use his sovereignty to allow humans to be involved in the process.  Obviously, almost by definition, allowing humans to be involved in the process of copying introduces the risk of error and even human attempts to “improve” the text.  Here is the bottom line, the New Testament is, by far, the most copied text of ancient literature, with the Old Testament being the only rival for second place.  Therefore, we have the ability to produce a text of the Greek with something on the order of 99.8% accuracy.  Our New Testament is extremely reliable.

As for Irenaeus, he was not a church historian.  He was a shepherd, a bishop and a highly influential church leader and author, but he was not an historian.  I believe that he was a very sincere Christian who did his best to defend the gospel and to defend genuine Christianity.  His reliability on historical claims will not be absolute, both because he was reporting what he had heard in some cases and because his principle concern was not as a historian but as a shepherd of the Christian church.  He is a generally useful and reliable witness to the history of Christianity and a witness of the state of Christian thinking in the second half of the first century, but I do not believe we can say that we can trust every statement he makes “without any shred of doubt.” And, by the way, there is debate about whether the statement “Father forgive them, for they know not what they do.” is in fact an interpolation. There is speculation that it is an interpolation, but the case is not settled.

John Oakes