One of the normative appeals of considering social cost in a judicial opinion is concreteness. Costs can be quantified. The very nature of a cost is that it is quantifiable, measurable, and tangible. That is an important element of judicial persuasion–basing a ruling on something tangible, rather than something abstract. The visual imagery of a “caste of uneducated children” (Plyer v. Doe) or criminals strolling out of court because of excluded evidence (Leon) or prisoners strolling out of prison because of overcrowding (Brown v. Plata, Alito’s dissent in particular) is much easier to visualize than abstract concepts of dignity under the 14th amendment and privacy under the 4th amendment, or the notion of regulating health, safety, and morality under the police power.
Thus, what judges are measuring is cost, not liberty or government power. It is very difficult, in the abstract, to quantify individual liberty, or government power. But it is somewhat easier–at least rhetorically–to quantify costs. With considerations of cost, judges, can put together well-reasoned opinions, quietly looking at at abstract values like liberty (and talk of dignity and such) and government (self-determination and such) but by actually looking at the costs, the negative externalities, of the competing value. This can be quantified, and can persuade.
I think this is an important element of why social cost is important. Or, it is my cognitive dissonance speaking as I try to prepare my job talk for interviews. Not sure.