Thursday, we heard them as people doing a job, probing, sparring, even joking. They could be tetchy, as when Neil Gorsuch cut off what he considered an evasive argument from Jason Murray, a lawyer representing the Colorado voters who challenged Mr. Trump’s eligibility: “Don’t change the hypothetical!”

Elena Kagan drew laughs from the courtroom when the Trump lawyer Jonathan Mitchell said that other scholars had noted an issue that she had raised: “Then I must be right!” she said.

The unfiltered live-cast gave audiences a break from the chatter and spin of 24-hour news. (The arguments in court were also respectful and focused, compared with the reports in other cases of histrionics by Mr. Trump’s lawyers and the client himself.) It may not have exactly been soothing, but it was a kind of respite.

The break was over when court adjourned. The networks reconvened their talking-head panels. And the subject of the proceedings emerged from Mar-a-Lago for another appearance, never one to let free media go to waste.

Mr. Trump’s remarks were half rebuttal, half campaign ad and 100 percent stream-of-consciousness. He called the case “election interference,” cited his polls, wandered from Ukraine to Israel to North Korea, opined on the value of his real estate and argued that he did nothing wrong on Jan. 6, 2021. (MSNBC and CNN cut from his remarks midway through. Fox carried them in full, with the chyron, “Trump: Supreme Court Case Was a Beautiful Process.”)

In Mr. Trump’s upcoming cases, of course, you will most likely still hear his self-defenses, attacks and re-election arguments. You will still get political counterarguments, legal analysis (well-informed or not) and hours of speculation and summary.

You’re less likely to get what you did Thursday: A chance to hear a civically important case directly, to hear and think for yourself, to take your seat as the 10th member of the bench.