Why Darius In Reality Is Broken
The concept behind Darius is a good one--create a character who's slow and bulky movements are outweighed by a powerful zone of offense within a short range around him.
Nobody has a problem with strong characters--we like strong characters. The problem is when there is no counterplay. Thus, in reality, the biggest problem isn't his abilities, his stats, his early game/late game; the problem is there is hardly any room for counterplay when going up against him.
The scenario is one we're familiar with--we have a strong opponent that we are gearing ourselves up to fight. We initially approach Darius the same.
He's AD; I'll build Armor. --You can't. At lvl 18 he deals 25% of your armor for free (before items) and his ult can deal upwards of around 1000+ true damage.
Okay. I'll stack health. --It matters little. Darius's level 5 Q on a roughly 3 second CD deals easily 600+ damage if struck by the blade, even when half of his items are tanky. He can aa-w-aa, since w is a reset; the aa's dealing decent damage (at lvl 18 it's easily 300-400-300 but more importantly applying the bleed) and the w being an empowered aa (as well as applying a 90% slow). Then of course the infamous dunk itself, dealing 1000+ true damage. Adding all these numbers up conservatively grants a 2600 (1600 Armor Reduced and 1000 True Damage) which means in a full successful rotation, he can thoughtlessly dumpster those with less than 2000 HP and with a bit of work, those with higher health (assuming that every target Darius fights is always at full health to begin with, which they aren't). It is fair enough that most any tanky character (with some exceptions like Mundo) might have 4k health at the end of the game meaning our 2000+ combo won't one-shot them. The problem with this inference is that if it's true. It's likely that the target hasn't been building a ton of damage. Darius at his core, is an anti-tank tank that excels at out-trading and out-dueling other tanks. If you've stacked health, you don't have damage, and he does. In a one-on-one slobber-knocker, he'll win.
Okay, I'll kite him. --This is probably the best strategy, but it's not without it's flaws. Kiting is generally the way to go, but in order for a character to have relevant poke, they must build damage, and if you are building damage you don't have HP (our one-and-only counter stat since Darius ignores so much armor). This means that if we kite back constantly, abuse our range and stay out of his--we'll win... in theory. The problem is that we have to work so very very hard to perfectly kite a flash+275-range-pull+90% slow(2x) and let's be real--most of us are human and NOT LCS material. And don't strike back with the "get gud" comebacks, because that's not the point--the point isn't that you can technically kite a Darius all day with the proper range. The problem is that the amount of skill required to always be ready for the flash, to always be landing our poke, to always be successfully csing while staying out of Darius's range is much, much higher than the amount of skill it takes to play Darius. You can brainlessly play Darius, make a few mistakes and still pull off a few effective plays. You can kite for days with Nidallee against a Darius, make one mistake and then get insta-gibbed. Additionally, if you are kiting a Darius, it means you have to have something to kite to--aka a tower. With your back to a figurative wall at all times, you generally going to arrive second when it comes to objectives because you don't have the initiative. You are the one who has to constantly be aware of your enemy's range--you are the one who always has to be kiting back to the safety of a tower--you are the one who always has to be wary of face-checking bushes (or at the very least warding them like we should be doing) for fear of the e-aa-w-aa-q-aa-r combo. Kiting means you are playing defensively, and as we all know, playing defensively is often not the best strategy in LoL. Lastly--and possibly the most frustrating--is the heal on Darius's q. In a perfect world, we are all kiting backwards, we are all staying out of Darius's way, and we are all not getting pulled in by him (or let's be real--his teammates--since we haven't even been including them in these equations). But none of us have ever played a perfect game of League, and certainly none of us have had a game where our teammates have played a perfect game--add to that, that not all champions in the game are ranged and not all champions in the game can poke and kite. It is very rational to consider that at some point, all that poke that you've landed on Darius--all that work you've spent the last 30 seconds gearing up for the big teamfight around baron--will become reduced or in some cases nearly removed by the heal on Darius's q, because someone got too close to him (a cc, out of position, or warding support is all it takes). The biggest counter to poke is heal--and guess what? Darius has got that.
Okay, I'll get him early game. --Darius doesn't have to have a good early game to be effective late-game. He's like the old Yasuo. My point isn't that you can't shut down a Darius early. My point is that the pay-off is not that great.
Okay, I'll take advantage of his low attack speed. -Darius doesn't need attack speed. He has an auto-attack reset, and as long as he lands his skills, he'll have more than enough bleed on you to give you the dunk.
Okay, I'll just dodge the Q by moving away from him. --This is feasible to do; but only if you have not been hit by his 90% slow, of which two of his abilities apply. You can't outrun his q when moving at 10% speed.
Okay, I'll just dodge the Q by moving into him and I'll get hit by the handle. --Wait... so you're telling me in order to counter a champion who's champion wrecking powers are unlocked when you're within 275 range of him, I should run within 275 range of him? No. The only time you want to implement this strategy is if you are going in for the kill. Otherwise, if you can't kill Darius faster than he can run through his combo, you're likely dead--and since he can build tank and has the potential to get 200 free attack damage (just think about that for a moment... 200 extra attack damage on someone who builds absolutely no damage items) killing him won't exactly be a quick process.
Okay, I'll take advantage of his ability spamming and wait until he runs out of mana. --Darius doesn't have mana issues. He might as well not have a mana bar. He doesn't need to build mana, his regular abilities cost 50 at max, and if he's spent his mana to use his ult, chances are you're already dead. Oh, and btw--at level 16 his ult costs 0 mana, so why does he have a mana bar again? Yes, he can run out of mana if he's just recklessly spamming his abilities early on, but... if you're fighting a Darius that stupid, you probably need to raise your ELO.
Okay I'll just... I'll just...
Darius is a character with 25% armor reduction, a true-damage ult that makes Cho'Gath look like poo-poo, a potential 36% missing health heal on a 3-second cooldown, potentially free 200 AD, a free damage over time, two forms of soft cc at a 90% slow, 1 form of hard cc at 275 range that ignores minions and can hit multiple targets, good clear/push with his q.... how do we counterplay against this guy reasonably?
TL/DR--Darius isn't unbeatable, it's just that he has so little counter-play that he might as well be, especially in solo-queue.