As a math teacher, I try to instill a similar idea in my students, and am glad to hear that the idea is useful in a broader range of situations!
In overstated form, my version of the idea is: “never use ‘it’”—because a student just learning mathematical language will have many different ‘it’s in mind, or, even worse, no clear idea of what ‘it’ is. (For example, I'll often see an application of the derivative summarized as “since it is negative, it is decreasing”, which is correct only if you change ‘it’s midstream—but students often don’t realize that they are, or should be, doing so.)
In overstated form, my version of the idea is: “never use ‘it’”—because a student just learning mathematical language will have many different ‘it’s in mind, or, even worse, no clear idea of what ‘it’ is. (For example, I'll often see an application of the derivative summarized as “since it is negative, it is decreasing”, which is correct only if you change ‘it’s midstream—but students often don’t realize that they are, or should be, doing so.)