Because it’s awesome. Full stop. I’ve been to many hearings and cases in district courts in as many opulent courtrooms as mundane office-like rooms, and none come close to the tangible grandeur of the Supreme Court. This isn’t to discourage attending a lower court if possible or there is interest in the court’s docket, just that the Supreme Court is it.
The Court’s calendar is known well in advance, so it’s very easy to know what’s being heard well before arrival. And once you know which cases will be heard, there’s a wealth of information and analysis about them to understand what issues are in play (nothing makes it all the way to the Supreme Court without lots of discussion). And even if it’s as mundane and unrelated to the OP’s interest, knowing just a little about the case unveils stories–actual people–behind them and understanding the importance to them and the rest of the law easily generates interest.
Many people are up all night anyway, just talking and discussing and, well, tailgating. Also, you’re not in the plaza itself, but wrapped along the sidewalk. Um, not that that makes any difference.
So no campfires, but if you tell even a middling camping store what you’re planning on (or post here), you’ll get tons of advice as to how to keep toasty (snowstorms, rain, cold snaps excepted), from battery-powered socks to disposable heat-packs and portable cots, it’s possible.
I’d ask if any current DC residents drive past the Court at those hours. I’m pretty sure you’re talking about four AM at the latest, but things may have changed. For a couple of the larger cases I arrived at ten or so the night before and it was too late. Not to discourage if overnighting isn’t in the cards, but I’d keep digging to find out, say, where the approximate cut-off point is (as in, how far down the sidewalk before you know no one is getting in). I used to know it’s general whereabouts, but it’s not exact as people are fluffy and sometimes two people would be ‘saving’ a spot for ten others.
Nothing ever came of spot-holding, but it’s a terribly shitty thing to do. You have someone at the rear of the line who camped out all night (it’s doable but not necessarily luxurious), when suddenly ten people here and five people there, all freshly showered and hotel-slept show up and fifteen people behind them don’t get in.
Not that you can’t come and go at all–it’s not elementary school–but it depends to an extent on who you’re next to–best thing you can do is bring coffee and a box of doughnuts for the people around you. That may also be another option gear-wise. If you want to bring lawn chairs and double-extra blankets and have a car nearby, you’ll likely be able to ask someone to hold your spot and go put them in your car. Again, I don’t know what the past five (oh crap, ten) years have done to security and the size of lockers, but if you can avoid issues so be it.
When I lived there this and the walking tour of the Washington Monument (did you know you can walk down the inside of the Monument and see all the commemorative stones?) were always the biggest hits from visitors–and I lived within walking distance of the National Mall.