In a 1v5 if they have to stop a siege, that's a pretty biased example. Not many tanks really have the damage to require being focused in that situation, and most often neither does Maokai, which often enough is why you won't see a Maokai try to stop them 1v5 because he'd rather just slow them down as much as possible with Saplings and wait for allies.
Now, onward: The job of the CC tanks is to not let you cross them in the first place. If we fiat the whole situation by saying "if you're able to bypass them without being CC'd" then you were going to win regardless because you just found a way to bypass the entire role of 20% of their team. This same sort of argument could be applied to your carry's damage capability: if we find a way to bypass his damage (in this case, by killing him before he can deal damage) then we invalidate his entire role and we make it significantly easier to clean up the rest of the enemy team with minimal casualties. The job of a CC tank is to make you think twice about how you engage, because usually their CC isn't something you can side-step, and Braum can't just be outright ignored because how are you going to find a way to ignore the guy standing between you and the carry with a giant shield that absorbs anything meant for the carry? You can't - you have to displace them by using a CC that could have otherwise been used on the carry or kill him outright. This is to say nothing of the CC he contributes to the fight. If you ignore Braum then you allow his CC potential to go unabated. You can't ignore him, you position around him and are mindful of where he is so you can bypass him - you aren't ignoring him, you're wary of him so you can get past his role as best as possible, which can often enough lead to putting yourself in a bad position or force your whole team to shift around. The dynamic of the fight was helped set up by what Braum can do and prevent you from doing.
The job of a tank, as I mentioned, isn't solely to absorb damage, but that does help: the job of a tank is to control the flow of a battle, which a CC tank does most obviously with their vast amounts of CC. However, those vanguards (Braum, to continue that example) can't be ignored because they'll still control the flow of battle just by the fact that they will forcibly position themselves to take hits for allies. That's not something you can say an enchanter does because they control the battlefield by avoiding anyone getting hit, whereas a Vanguard makes sure that if anyone does, it's them. And you can't ignore any of them, you have to be wary of them and work around it. That's part of the job of a tank. And yes, they do share that kind of role with controllers and enchanters. They are the more physical and direct embodiment of the role, if you want to get on that level. Not very easy to kill a carry when you're being repeatedly slowed, or stunned, or knocked back, etc., and it's also hard to kill them when there is a direct wall between the both of you that comes packaged with his own CC for peel as well.
You don't tend to ignore a tank, you're wary of them and work around them, which is something they can work to their benefit through coordination with their team. Even if they're the last one alive, you can't say you ignored them unless they screwed everything up so badly that they could be ignored in the first place. You had to minimize his impact knowing what it could be in the first place, and in the case of a CC tank that tends to be much more difficult. How often do you just "walk past and ignore" someone like Alistar and Amumu? Not often given the nature of how they work. You have to devote something to them. They do their job, and if they're the first one in, especially as Amumu and Sejuani tend to be, then they have the tankiness to continue to survive long enough to contribute further damage and CC.
Now, you had a point brought up about how you'd never target them over someone else, and my retort to that is: when would you ever prioritize someone over the carry that isn't a healer if you have the chance? Tanks are no special exception to that, it's just that they're there to make sure you don't get to have that choice at all. I wouldn't target a Maokai, for example, over a Vayne if the choice was there, so based on that Maokai is also not a good tank. In that setting I'd only choose Maokai over Vayne if there was something preventing from getting to Vayne, but until then I'll have to hit Maokai so he doesn't disrupt even more of my team. Which is the job of a tank, and more than just Maokai can do that. Leona is a pretty good example. She probably won't directly kill you, but unless something is done about her then she will continue to output some CC throughout the fight and make it generally a pain to do anything about the rest of her team, and if she latches onto a carry then that carry has to get away from her or risk contributing nothing amidst the CC of Leona - Leona, despite not having solo kill threat damage, has become a focus on the back of her CC.
(btw, don't think I instantly think you're wrong or don't understand your perspective, this is just mine and how I see it in games. I'm liking your perspective and how you see this whole situation.)
can ever do and 1v1 them without getting any peel, like they should need to.
are not worth buying on ADC cuz they have no crit.. #ADClogic?
