The first reason why an understanding of productive labor and the Marxian categories is indispensible (and far superior to bourgeios categories based on neoclassical theory) is that exploitative nature of capitalism can't be understood without them. Productive labor creates surplus value (potential profits); unproductive labor uses it up. In studying the contradictions of capital, its important to know the difference. Each kind of labor performs different functions for capital, and each leads to different kinds of contradictions. More than that, since the creation of surplus value *defines* capitalism--it is its defining distinction as an historical system--it is important to understand the origin of that creation.
More particularly, an understanding of the category of variable capital (as measured by the social subsistence of productive labor) exposes the unequal exchange that occurs in the labor market. Productive labor receives its subsistence; capital accumulates the surplus value.
No similar understanding of the nature of capitalist exploitation is possible using published stats. For example, all wages, salaries, and fringe benefits are lumped into "employee compensation", that catch-all bourgeios category. Any class basis for labor has disappeared. If Bill Gates pays himself a salary at Microsoft, that's part of "labor's share". Using bourgeois data, then, what can we conclude about "labor's" share of net product? Is it "fair"? Is labor being exploited? Does capitalism exploit?
Without recourse to Marxian categories you are mostly left to whine that corporate executives pay themselves too much, based on some pay standard you must concoct. Is this your idea of exploitation? Do you see the difference between arguments like that and a marxian discussion of exploitation at the heart of capitalism as a system? You say you believe that profit originates in exploitation, but without a grasp of Marxian categories, what is the basis for that belief?
And if the Marxian categories are the basis for your understanding of capitalist exploitation, why would you want to abandon them in analyzing the laws of motion (profitability or growth theory)? These are not separable topics. Exploitation and the laws of motion are ineluctably intertwined. A clear understanding of the nature of capitalist exploitation logically leads to a pursuit of contradictions as capitalism develops based on the same categories, doesn't it?
You pose a particular question: Given some level of exploitation, you want to know in what ways the Marxian value categories differ from their bourgeois counterparts in analyzing the trends in profit rates; what can they do that bourgeios categories can't. Well, I am happy to walk down that road with you, using established statistics.
Perhaps the best way for you to see the difference between Marxian and bourgeois categories is to set them down side by side, and examine how they are produced. I think it will then be obvious to you how the analytical possibilites differ. Because they do. A lot.
Marx has constant capital, variable capital and surplus value. Bourgeios stats have capital stock (typically measured as net capital stock), employee compensation (wages and salaries), and profits (more precisely, after tax profits), all typically of nonfinancial corporations).
We can quickly dispense with the categories that are most similar: constant capital and capital stock. In dividing the product of a production round (say, one year), the amount of capital used up is subtracted, leaving that to be divided between capital and labor. Bourgeios stats call this capital consumption allowances. The Marxian term, circulating fixed constant capital (sic!) is similar, though there are differences in conceptualization. Mainly though these have to do with accounting for differences in fixed capital turnover time (changes in average asset life affect profit rates). But these are relatively minor effects compared to the differnces in the other two categories.
As to variable capital and emplyee compensation, the differences are obvious aren't they? Employee compensation is a worthless category if you want to understand the basis for capitalist contradictions. Variable capital allows analysis of labor by the function it performs for capital, to uncover the contradictions sprouting from that process. For example, unproductive labor is paid out of surplus value. Needless to say, all class distinctions are missing from employee compensation.
Now we come to the biggie--surplus value vs. property income (profits+interest payments) In published data, property income is what capital says it is; i.e., what it can't hide in employee pay and perks, lavish office buildings (as capital stock), or a myriasd of other dodges, and allows to be taxed. In this sense, published profits + interest payments is not an measure of profitability. Capitalists choose to take "profits" in many forms. Does it matter to the laws of capital in what form Gates and others take claims on Microsoft and other giant corps? Absolutely not. Does it affect your study of profitability using bourgeios data? Sure can. So you can track movements in published profit rates all you want (and I've done that too). But please don't fool yourself into thinking you are making much headway in sorting out the contradictions of capital.
In contrast, surplus value is a residual. Its everything left after the reproduction cost of constant capital and productive labor has been accounted for. It is, in this sense, all *potential* profit. And it's a roadmap for all the ways capitalists have struggled to keep the system running. In Marx's day vitually all surplus value was realized as profit and accumulated. As the system grew and confronted contradictions, surplus value began to be be realized in other forms. But each solution of this kind produced new contradictions. Today a relatively small, and shrinking, share of surplus value is realized as property income. A few days ago, I argued that one of the things this means is that locus of the (class) struggle over surplus has shifted to many fronts, from the simple, production based, direct confrontation in Marx's day. But I only scratch the surface.