The Intellectual advises both breadth and depth at the outset of the intellectual life. This may seem contradictory, but only apparently so because breadth is advice against specialization, while depth paradoxically allows for more breadth. What Sertillanges means by breadth or "comparative study," is "widening our special work through bringing it into touch with all kindred disciplines." What I believe he has in mind practically is that the economist, for example, should thoroughly know Catholic Social Thought, the philosophies that pertain most to economics, the historical circumstances that produced modern economics, the statistical know-how to engage other economists, etc. Wall Street is a clear example of historical ignorance, or at least blindness, as the continual cycle of booms and busts still confounds everyone despite the clear historical evidence that economies are cyclical.
There are plenty of reasons for "comparative study." Sertillanges cites a few: the connections between disciplines, the biases of each discipline, motivation of the intellectual and the example of great intellectuals. We all understand the interconnection between disciplines and that great intellectuals were people who mastered many areas. But, it is worth reviewing the Intellectual's list of biases for each discipline:
"Mathematics by themselves warp the judgment...physics, chemistry, obsess you by their complexity and give no breadth to the mind...physiology leads to materialism, astronomy to vague speculation; geology turns you into a nosing hound, literature makes you hollow, philosophy inflates you, theology hands you over to false sublimity and magisterial pride."
While I cannot speak from experience about the biases that Sertillanges asserts about all the disciplines, I can recall conversations with economists in which philosophical questions came up and were ignored as unscientific or "scary." This leads to economists boiling down the individual into a "profit maximizer" ignoring the infinitely complex reality that is the human person. E.F. Schumacher explains this beautifully in his essay "Buddhist Economics" in Small is Beautiful.
It's worth looking more closely at how greater depth leads to more breadth. "By approaching the center of all ideas, everything is simplified." In other words, if we aim for the fundamental principles of a discipline, then different disciplines start to converge and we begin to see similarities. "The different branches of knowledge are the different languages...and to decipher several of these languages helps each of them, for at bottom they are one." I cannot speak directly to this phenomenon because I have not experienced it in a deep way, but I can say that even a superficial study of different subjects reveals patterns that apply across disciplines.
*quotes are from "The Field of Work" section I