Is it? Because the marksman duels in my games tend to last 5-7 seconds, depending on how committed each is to stand and trade.
yes it is. You are taking one situation and comparing it to an average of many other situation that are similar.
Then put it this way. Imagine if a Samurai could kill a Paladin in less than four seconds. The Paladin wouldn't matter anymore. It'd be obsolete.
The Paladins job is to CC and absorb damage to allow the paladin's allies to kill the Samuri. (I think this is a terrible analogy, but I will use it to try to get you to understand)
So you're telling me that literally the only thing a DPS should be able to do in a teamfight is kill the tank. After that what, they run away? Because if anyone with a modicum of damage gets on them, they're toast. Come on, you've been at this about as long as I have. You should know the triangle.
I'm saying that the DPS is the best at dealing with the tank. The job of the DPS is to dish out as much damage as they can while staying alive and safe. After they kill the tank they focus the next safe target to attack and so on.
Marksmen hit squishy and annoying enemies.
Burst-damage mages hit marksmen to destroy them before they can do much damage.
Marksman hit anyone they can safely. Preferably squishies because squishies do more damage than tanks and can kill marksman.
Burst mages focus marksman so that the marksman can't do their one job do consistent damage.
Tanks are hit by both, because their job is to soak up damage. Brawlers fight back, pure tanks don't so much, but that's a stylistic choice; overall a tank's job is to soak damage from all sources so their marksmen and mages can do their job.
Yes and Tanks and even brawlers to an extent want to apply CC to those opposing damage dealers(Marksman and mages) so their damage dealers can safely kill them.
The idea is that Marksmen or Mages could theoretically kill one another rather quickly, coming down to a variety of factors.
Yes, but it is not theoretical it is fact.
That's where the tank steps in, and this is why the tank has long been the crucial element in teamfights.
Kinda two separate thoughts so I split them up. In a teamfight scenario Tanks are super important like you say.
He who tanks better allows his team to breath better, and that's where the teamfights are won.
I think you miss a lot of important elements here. Tanks jobs are different depending on so many different factors. To tank better can mean so many different things and even if you play the fight better as a tank you must rely on your teammates to play it right as well.
Lucian can kill a tanky Leona is 3.8 seconds, she's not giving her team any breathing room, and this isn't how it used to be.
Alot of things here. One, Leona had to have not landed a single ability and not had her W up to die this quickly. In other words she tanked wrong, and deserved to lose. Leona is also a support tank so she is drastically squishies than a true solo lane tank would be at this point.
You've been here since Season 3, you know this. Yes, Season 5-6 was a little too tank-leaning, but allowing them to die in four seconds is the epitome of over-correction.
Seasons 5 and 6 were WAY too tanky. Don't underplay it. Yes right now tanks do feel weak, but again with a few adjustments to those high true damage numbers I see them coming back strong. They also need to help them by making the resolve tree not trash. Tanks need to rely on their team and that has not really been seen until recent. Yes they may be a wea bit on the weak side, but they are much closer to where they should be now than they were in season 5 and 6.
and Tanks honestly just need maybe some nerfs on champion that have too high of true damage. Not items or runes, but champions like 
with 1k true damage on her Q and things like that.
