Taking a look at St. Irenaeus' writings and the history of their use
I must admit, Doctor of Unity doesn't feel like quite the right appellation, but I am struggling to think what would be the right one. On refuting the Gnostics, he is invaluable today as we see a return of Gnosticism. Doctor of Orthodoxy I imagine wouldn't go down well, but that's sort of what I'd like to call him.
The weight of one thing over another, as in historical effects of Church division and unity, don't work with Irenaeus because they're not an essential measuring stick for a doctor of the Church. Also, the refutation of Irenaeus as ambiguous on some subjects could be high praise rather than worrisome analysis.
I'm not dismissing academic analysis, but setting it aside in these matters. The assignment of Irenaeus as a doctor of unity simply fits the Church leadership's current agenda. A look at the designations of earlier doctor's "specialty" can also seem to more fit an agenda than signify a saint's perspective.
Any doctor's written works are not scripture and display everything from musings to errant, likely parochial thinking. Irenaeus's importance may not equate him to Aquinas, Thomas, or Teresa of Avila. Equality, again, is not a measuring stick for doctors.