To some degree these fights can be punishingly brutal on healers... Naj'entus in particular is a fight that is made or broken on the back of your healers... and the tank/healer synergy is as always most clearly seen when learning them for the first time. As a tank you have to come to anticiapte what your healers can and can't do so to know when to use whatever panic buttons you have available or gear in whatever way you can to make life easier on them. Are you going to have to go a long time without a heal while the raid tops everyone up? Are you going to have to catch the boss mid phase shift with your healers scattered around the room? You and your healers are cogs that have to mesh to make for a successful first kill on a boss.
The relationship between DPS and tanking is at once incredibly basic and rewarding in its complexity. It's been said over and over again that without the DPS you can't kill anything and without you the DPS gets killed, but in fights like Archimonde you can witness a complex series of factors that entirely remove the 'tank and spank' paradigm and force everyone to be mobile and alert. Since even one death can provide the boss with a Soul Charge (they come in three flavors, too) your DPS has to provide their consistent damage while avoiding fears and doomfires and air bursts, meaning that you can't take them for granted or assume what they're doing isn't hard. A lot of fights basically hang the DPS out to dry while you're getting the lion's share of the healing, and if enough of them die, you can forget killing anything.
Let's emphasize that: if the DPS die, forget killing anything. Yes, it's true that DPS should be disciplined and avoid pulling aggro, but sometimes it happens. You might make a gear shift in favor of stamina or avoidance over threat, and it may not be properly communicated to the DPS: such a change happened on our last Naj'entus kill, where we were short healers and so I stacked dodge and stamina over hit and expertise. I did in fact become easier to heal, but we neglected to inform our shadow priest that my threat generation was going to be down from what she's used to me putting out. Suddenly her comfortable threat threshold was about 200 TPS lower than it usually is, and her death was entirely due to that oversight on our part.
First attempts on a boss are always chaotic. Even if you've read a lot of strategies (my guild tends to go in fairly blind, sometimes reading up on a strat if it's a infamously hard boss but otherwise finding out by doing, since we figure that's how the first guilds into these fights had to experience them) there's a world of difference between reading up or watching kill videos and actually seeing a fight for the first time. Videos are rarely shot from everyone's perspective, for instance, Mobs may path in unexpected ways, you can misunderstand which mobs you're meant to tank and which ones you should CC, they can hit harder than you expect, your DPS can kill Channelers a lot faster than you expected so that you only have to tank a few Defenders... you won't really know how these things go until you see them.
I'm using Shade of Akama as my example here because it's a fight that can require multiple tanks, yet at no time are any of these tanks tanking a boss. A tank at each doorway to work with the CC to keep the constant spawns locked down or killed, and a tank next to Akama to pick up Defenders as they run in, eventually tanking quite a few of them (this is how our strat works, of course, you may do it differently) but at no time are any of these tanks the center of attention. You're just there to do what has to be done to get the boss down, same as anyone else.
It may be the best fight in the game as far as teaching tanks something they can often lack: the humility of awareness. You're a cog in a machine. There's no one hero in a raid group. You may save a raid with a fast pickup from time to time, and that's great, but in the end you're no more important than that rogue with the consistently high damage or the healers who keep you all alive so you can keep the mobs off of them so that they can be killed. It's all part of a mechanic of strategy you all take part in, and going through any fight for the first time you can really observe the machine coming together. You can detach yourself and watch as the tanks figure out where to take their mobs, the CC grasps which ones are the most dangerous and need to be locked down, the DPS improves in mobility and efficiency and gets the channelers down faster so that less defenders spawn before Shade comes out, and then that final burst of raw raid-wide DPS while one lonely tank stands next to it all, tabbing between defenders to keep them off Akama.
In one night you can go from wiping to standing victorious over a boss you've never seen before, or it can take you weeks of effort to finally kill a boss. Each raid is different, each fight a new experience. I still remember how it felt to kill Kael'thas finally, after a longer time than I wanted stuck on that fight. To look and see that everyone was working towards that final, glorious moment when he would finally be dead, that we all finally understood the fight, knowing it would happen when three DPS players brought me the Shield without even being asked or told to just because they knew it had to be done, and they wanted to make sure I got it. When the machine is working properly, it's a thing of beauty and you don't need to be the center of attention, don't need to convince yourself you're all important. You're happy just to be a part of it.
Of course, a little ego is necessary to be a tank. Trust me, you'd probably not endure it otherwise. But that's a post for another day.