Would you call it a "living document" (or set of documents) somewhat like the US Legal system which has evolved over time?
Yes. I think that's a very apt comparison. I might even stretch the analogy thin enough to say that the Torah is a bit like the Constitution, which, generally speaking is not changed, and when revisions are made, the revised text is still printed as a part of the whole, in order to teach, and for reference in case jurisprudence indicates that a revision to the revision might be needed. The Talmud we could compare to the Federal Statutes, and post-Talmudic rabbis to Circuit Court and Superior Court judges, with the halakhic literature being equivalent to the body of Federal, State, and common laws. I mean, that's stretching the analogy to the breaking point, but I do think you've hit on the notion that in order to be a legal system for a living society, the law itself must live and breathe and evolve, so to speak, with every case brought before a judge, and with every evolution in society causing us to reconsider our social norms and frameworks.
In the case of halakhah, the religious nuance to this idea is that revelation is ongoing, not static, and as we (hopefully) grow and mature as a species, as a people, as social individuals, we are able to unfold new and more refined understandings of how God wishes us to pursue justice, compassion, and faith. There is a saying in Rabbinic writings that the Torah has "many faces," or that "everything" can be found within it, which is of course not literal, but a metaphor for the idea that a truly revelatory text can be interpreted, reinterpreted, and reinterpreted again, to a nearly infinite extent, because its sacredness and potential reflects in some small measure the Infinite and sacred nature of God who either inspired it or gave it (depending on one's interpretation).