Actually, I'll go over every point you made kindly and hopefully you won't just rudely write me off as a "Zed fanboy" and zealously say I'm denying the truth.
Insane Damage - Yes, single target, anything else is just average.
The ability to attack from multiple angles - Technically yes, however typically it is from one angle since throwing a shadow to the side doesn't increase your range by much which defeats the purpose of blowing your safety. Very rarely will you have all 3 shadows out and somehow coordinate some sort of super angle attack. Like once in a blue moon, rarely.
Great Aoe Clear - Yes
Energy - Yes
Bonus 10% health damage on hit - This is his max level passive that will only proc once every 10 seconds on a target if they are below 50% health. So, you are correct in this, however you are exaggerating it and making it sound much more than it is.
Leveraged AD - Yes, off of bonus AD.
Spammable Aoe Slow - No. He can only slow with his shadow's e. You can get a maximum of two e's in one shadow's duration, and it has a very small area around the shadow. People can see the shadow and not go near it. It also costs energy each time. A W-E-Q-E combo will drain your energy. It is not spammable, you can use it twice at full energy if they decide to sit in the shadow for about 3-4 seconds.
(E) Casteable while moving - Yes. I don't see the issue with this one. It would need to do more than some simple damage if he had to stop and twirl around in the small range it has. In fact that would break his ult's damage.
The ability to leverage the damage dealt by active items - Yes. Namely bork, an item that gives +25 bonus AD, 40% attack speed, and some percent damage on hit. This hurts his w's passive and gives him less AD to use on his spells, and death mark's actual damage. It all balances out. Ravenous hydra gives lots of AD but it's a melee cast range and it gives less than an auto attack's worth of damage as well as not being that great of an item on Zed anyways.
THREE dashes (4 with flash) - Not quite. You're thinking of gap closers, yes. He can shadow, he can ult, he can ult back to shadow, and he can flash. His shadow "dash" takes a tiny bit of time to prep, not an instant dash like lucian or riven. The shadow has a missile speed. If you really want to consider his ult a mobility mechanism, I think you would stand alone on that. I think Zed would fall off if he had to be in auto attack range to ult someone. Zed's ult shadow is also not necessarily a mobility mechanism. It appears where you ult from. Sometimes, yes. That shadow is fairly far off. And sometimes, it's right on top of the person so when you try and ult back to the shadow, you went nowhere. And no, you're not "bad" if this happens. Often you can't avoid ulting when you're right on top of the person. You're over-exaggerating his mobility with the "4" dashes he has with flash. At most he has two.
Highest Base Movement Speed - No. 355 is the highest, there are some 350 as well. This is not "subjective" as you claimed us zed mains to be, it is fact.
Invincibility - No. Zed can time his ult to dodge a spell, correct. This is not invincibility, this is a dodge. Invincibility is Fizz and Kayle. Zed has to use his ult to dodge anything which has a long cd compared to fizz's troll pole. Kayle's is an ult too, but it's designed for it therefore getting much more time. It is not easy simply dodging a spell with his ult. It requires timing and actually having your ult up. He is not simply "Invincible" as you worded it.
The Ability to increase his range - Correct. With the use of two spells, a lot of energy, his mobility, his safety, and a long cd, Zed too can momentarily be a Xerath. And then when Xerath's q comes back in 5 seconds, Zed's shadow does not. This actually has huge counterplay. If Zed uses the shadow for a long range harass, coordinate with a jungler or get your own harass ready. He's not escaping for a solid 10-14 seconds. Plus this long range harass is a skill shot and if it hits anything besides you first, it will tickle. There are many factors that go into this "boon" for Zed.
2075 units - Correct. If you blow every piece of kit he has to be as flashy as possible (no pun intended) just to ult that guy, he can achieve this. Once every 300 seconds. Except his ult's damage is lowered because you no longer have a shadow to help you do some extra q damage/pursue.
The Ability to amplify his teammates damage - ...what? I mean, yes. There is a mastery or two for that. I think it's for every basic attack, his team does like 1% more damage up to 3 stacks. However, I assume you're referring to the fact that his ult uses the damage done by his team too. No. It is only him. Only the damage he does, not including ignite, is factored in.
Overall, I'm going to assume that you main ADC or a mid and have not actually played Zed. The fact that you think he is the fastest in the game, amplifies his teammates damage, and that he has a "spammable slow" leads me to believe Zed is not your most knowledgeable champion, and that's ok. He's recently gained huge popularity with nerfs to other assassins, and it can be easy to just throw hate at a very played champion. Zed has very realistic counterplay, and he is also a very powerful champion that is counter play. If you play mid vs him a lot, pick up an early armguard into zhonyas. Zhonyas is very useful versus him. If you adc, QSS. It gives MR, correct. But it cleanses the ult as well as lowering his bork and passive damage. Plus, putting it into mercurial scimitar gives some nice AD as well as an ms boost when you use it. Also rely on teammate peel. If you're an adc and you're complaining you can't 1v1 Zed, you are indeed correct. It would be overpowered if you could. He is supposed to counter you, however he is not necessarily supposed to counter say you and leona, or you and thresh. Assassin's are there to kill the squishies, not the other way around. Unless you're really fed, Zed should win but that's why Riot implemented the teams of 5 system and didn't make this a 1v1 game.
Overall, don't downplay Zed's difficulty and weaknesses. He's not just a bunch of button mashing, well at least not in higher elo's. Instead of complaining and fabricating some claims on how he's op, sit back and just think to yourself how you can counter it. If he was so broken that there was no counter, there would be a hot fix. If you're an ap mid, think of how you can position yourself in lane to lower/dodge his damage, what you can build, how you can harass. IF you're adc, think about how you'll be positioned in relation to your peel, think of a reaction when he inevitably ults you. IF you're anyone, just think about "If Zed Ults me now, what can I do" and when he finally does ult you, you should have a plan whether it be flash, or an ally's peel, or hell your own peel (Looking at you Veigar). Hopefully this post can sort of enlighten you a little bit on Zed and maybe detract some hate you have from him.
Or you can wave it all off and call me a fanboy and say I'm denying the truth. And hey, if you can't beat 'em, join 'em. Go and buy Zed and absolutely crush your way to challenger if you believe he's that good! ^_^
and just R and auto somebody once for a 1700+ damage crit while also lifestealing back to full.
