Judge Posner's rhetorical flourishes are more entertainingand, toward the end, more revealing than perhaps he might wish.
Judges are likely to cite foreign decisions for the same reason that they prefer quoting from a previous decision to stating a position anew: They are timid about speaking in their own voices lest they make legal justice seem too personal and discontinuous. They are constantly digging for quotations and citations to support positions they've adopted on grounds other than the compulsion of precedent. In-depth research for a judicial opinion is usually conducted after rather than before the judges have voted, albeit tentatively, on the outcome. Citing foreign decisions is probably best understood as an effort, whether or not conscious, to further mystify the adjudicative process and disguise the political decisions that are the core, though not the entirety, of the Supreme Court's output.
This is not surprising from a judge who says that his philosophy of judging is "pragmatist," rather than "formalist" or "intentionalist" or anything else. What it unwittingly reveals, though, is that the hierarchy of authority in law is intellectually dubious at best, and quite possibly actively dishonest at worst. Too many decisions, and more importantly later citations to those decisions, founder upon false dilemmas, worst-case analysis, ad hominem argument, the straw-man fallacy, and other logical errors. Once the error becomes authority, though, judges shy away from pointing out such fundamental flaws, regardless of the source. Criticism of authority ossifies to criticism of factual context. That's not good for anybody; and it smacks of blindness at best, and possibly darker problems.
This is aside from the inherently reactionary nature of a system of law based on prior authority; predictability does have its virtues when planning one's course of action. My fear is that as the rate of social, technological, and cultural change continues to accelerate, those "well-seasoned precedents" are going to become less and less relevant. For example, McPherson Buick's approach to determining the proper payor for mishapsdoes the total cost of avoiding related mishaps [significantly] exceed the total cost of related mishapshas been seriously undermined by more-recent work in economics. Nonetheless, McPherson Buick is the economic approach taught in law school, and thereby becomes self-perpetuating.
This, in turn, brings us full circle to the real question that underlies this disagreement: How much weight can we give to argument in different contexts than our own? This is where both sides founder: their failure to recognize that the past and future are as much foreign cultures to us as are those of other nations.