Assassins, by their nature, are kill the MVP champs, rather than kill the team champs. They're all burst and no sustain.
In my mind, Kat is the exception, because she's a reset champ. I have seen Fizz and Talon make pentas, because they have a fair amount of AoE damage, but they are way worse at it than <insert fed bruiser or marksman here>. Taken to the extreme end of the pool, I don't think I've ever seen Shaco or LeBlanc make a pentakill.
The failure mode with strong assassins is every bush containing something that makes you instantly dead, not someone who makes it impossible to teamfight. In fact, early grouping is usually the way good teams play in an assassin meta, and someone like Zed responds by split pushing rather than trying to teamfight.
I would argue that a strong assassin killing your MVPs is exactly that: Killing the team. He's not literally 1v5ing, he's killing your carries and then dancing away. Even if he dies doing so, he's removed any capability your team had to fight, and the assassin's team still has its carry, whereas yours either doesn't or only has a bruiser/fighter, and he can't deal with 2 carries and your support+tank alone, even with his team's support/tank backing him up.
To put it another way, Shaco and Leblanc don't need a pentakill: They need picks, and strong assassins make it infuriatingly easy to get them. You have massive outliers like Season 2 Akali (where she'd just shit on everyone) but usually when an assassin is 'too strong' it's due to them being able to effortlessly pick off your MVPs and more often than not escape, but it's not the end of the world if he doesn't (because he's hamstrung your team.)
I would like to point out that I'm talking primarily about Solo Queue and not teams. Although I don't doubt that Diamond+ players will do exactly what you suggested, the vast majority of the playerbase, well, isn't that good/smart.
I think bruisers are inherently more frustrating than assassins. With assassins, you get this "argh I can't catch him" thing, but that feels better than "he's tankier and more damaging than me, I just got right clicked to death" thing the ahead bruiser has.
Better isn't good, but it's really hard to make losing feel good. To the extent that losing feels good, it feels best on mages with high skillcap ability use.
Bruisers are their own entire post worth of balance issues that I'd love to go into in greater detail at some point. However, the 'argh i can't catch him' thing is VERY often worse than the 'fuck this meatslab of bullshit' thing, because the 'argh i can't catch him' is ALWAYS preceded by 'an ally has been slain', signalling that you're not teamfighting for the next minute or so, and their team just got the go ahead to take dragon/objectives/free cs/baron/force a fight.
Bruisers don't have that. They'll bulldoze your ass, absolutely, but assassins are more insidious and more of a pain in the ass than bruisers are. It's easy to see where bruisers need a nerf bat to the balls, assassins less so.
Not to disagree with you, though, I completely agree that bruisers are equally as problematic, if not more in many situations.
There's actually a lot you can do to avoid Zed making the kill. There's just not much you can do to punish him for it. His ult cooldown isn't even that long. It's the dive equivalent of Nidalee spear spam.
Yes, I know, and perhaps i phrased that portion of my post incorrectly. My intention was to state exactly what you said: You can't punish him, even if you avoid dying. Sure, you can pop Zhonya's or use QSS to cleanse the ult. That doesn't mean you're going to be able to put a few holes in the shady bastard.
Which in turn comes from bruisers causing teams to need super powerful ADCs. This is the old DotA chestnut, where everything is OP so nothing is.
This meme needs to go away, for several reasons. I play DotA, so I know from experience that this is bullshit.
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DotA has a lot of its balance tied up in item trees. A ton of counterplay involves the items, and how to play around those items, or how to counter items with items. It's a lot deeper than 'buy void staff against MR stacking tanks' or 'buy armor vs physical damage'.
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Heroes have BLATANT strengths and weaknesses (again, many of which are tied to items.) Riki is a massive noobstomper, but buying Dust of Appearance basically shits on his parade. Carries can be super irritating, but if they're careless they can kill themselves because of Blade Mail. So on and so forth.
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Power is different in DotA. There is no scaling. Some heroes, like Skywrath Mage, do get some scaling from stats on their abilities, but nowhere near the kind of scaling League has. You're not going to see Lina ult'ing for 3000 damage because she's full build: that damage is static (with the exception of Aghanim's upgrades, but that's a different story)
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Continuing on 'power is different', the map is also different: Blink Dagger would be GAMEBREAKING in League, the map is TINY compared to DotA. Blink Dagger is basically mandatory in DotA for a very large selection of heroes because of the size of the map and the short range of many abilities (such as Axe's Call or Magnus's RP.)
I could go on for hours about this, I really think this meme does DotA a disservice and is used as an excuse. It's just not true.
As for your point about needing powerful ADCs to stop bruisers: When it comes to ADCs I feel like the community gets into circular arguments.
Bruisers are OP, therefore we need ADCs. Without ADCs, tanks/bruisers would be OP, so we need ADCs. Teamfights would be too slow without ADCs, so we need ADCs.
That kind of thing. People find all kinds of reasons to justify class power, every class has players that do this. Assassin fans will claim that their champion is squishy or is up shit creek if they mess up, Bruiser fans will claim that their champion is weak early or is vulnerable to split pushing or such and such, Tank fans will say 'don't focus the tank', and so on.
The justification doesn't mean that the class isn't problematic: It's an excuse.
We bounce from bruisers to marksmen to assassins being the defining class, typically it shifts a couple times a year. Right now we're in a marksman meta and have been since about June.
I think the game actually works best in assassin metas. You end up with a heavy roaming and high surprise factor game when assassins are strong. When bruisers are strong, you end up with a camp top lane meta and lots of snoozey split pushing.
I can understand that. That's a valid point.
I don't really think the game is out of whack. I just think people like complaining when they lose, and half of all players lose. If we could somehow make it so that 2/3 of players won every game, we'd be in business.
I think mobility creep has been tremendously positive for the game. It's created quite a few problems but the gameplay is more fun, varied, and skill testing.
Losing is certainly a part of it. However, as for mobility creep I feel that Riot could take steps to mitigate the disadvantages and maximize the advantages from a powercreeped League, and they haven't done so. There are legions of champions that lack mobility, or need tweaks and fixes to deal with mobility in their own way, but Riot just keeps on pumping out new mobile champs while playing whack-a-mole with the latest FotM.
right now, and this list is a lot longer than it was in season 3.
has more problems with 
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(I mean the active is ridiculous, stealing movement speed from a target is way too strong in this mobility creep meta), but it doesn't really matter, because as long as people feel helpless to prevent a zed player from outplaying them or not, but still getting the kill, they will scream op.