Which means: when it comes to D&D, I usually prefer to err on the side of simplicity.
Now, one thing I actually like in old school D&D that is a lot MORE COMPLEX than WotC D&D is the intricate initiative system that we see in AD&D (and probably OD&D, BX etc, although AD&D is more detailed - there is a famous 20-page document trying to make it SIMPLER). Although it might be unclear and not easy to understand, the ideas behind the system are in many ways a lot more intuitive - and sensible - that anything WotC has used in their games.
Modern D&D initiative is mostly an abstraction without footing in the real (or fictional) world. It often feels "fake" or artificial - even tough I find it good enough to just ignore most of the time. This has nothing to do with "Greyhawk initiative", BTW, who feel more gimmicky than real IMO, although its goal is probably the same as mine.
Old school initiative, on the other hand, tries to reflect what would REALLY happen in a battle. To see what I'm saying, try to picture a fight. Not necessarily in a boxing ring, but IN YOUR IMAGINATION - maybe with monsters, and spells, and swords, and missiles.
First, the parties would see one another and quickly EVALUATE the other side (are they approaching fast? Are they scared? this is the declaration phase, BTW). Distance would be vital - if they're close enough, the thief might stab the enemy wizard before he draws his magic wand. If one side is using bows, they might get a shot or two if they are far enough, but once the other side closes in... the bow is nearly useless. If parties are reasonably far, one side may choose to flee before the other side can reach them - unless the other side has bows or spells. If both want to fight, who moves first doesn't matter - its all about who strikes first. One could always say a few words before getting pursued and hit, but a spells might take a few seconds to perform - can the barbarian reach the Wizard before his allies are hit by a fireball? And so on.
This is what initiative is for - the action, the tension, the tactics, the randomness and unpredictably.
Most modern initiative mechanics have no function in the fiction: there is no reason why the dexterous character should act before someone who is smarter or more attentive, for example, and there are mechanical incentives to do things that would make no sense in the real (or fictional) word, such as staying 35 feet away from you opponent for the fear he might approach and attack before you do anything at all.
Anyway, let me illustrate my point to be clearer.
Imagine your PC is a soldier of the blue faction, walking down a road. The GM says: "you see a red soldier turning a corner... you're 30 feet away from him... roll initiative!"
GM: "He rolled 19! He walk to you and attacks you three times!"
PC: "Huh... okay".
Some situations can get even more ridiculous. Say you can move 30 feet, for example, and you're 50 feet away from your enemy, both with no ranged weapons. Nobody wants to approach first - since this means you cannot hit your enemy but your enemy will be able to hit you, even if you're holding a long sword and he is holding a dagger.
Or imagine your enemy is prone (in 5e): if he wins initiative, he can stand up, walk to you, and attack you a couple of times before you can do anything.
Not to mention silly things such as the infinite line of fighters: fighter A moves and strikes fighter B, who then moves and strikes C, "ad nauseam", covering the space of a mile in six seconds.
How should an actual fight go?
If both sides want to fight, both should approach at the same time. Then they would exchange blows. Any side with ranged weapons might have a change to attack. The longest melee weapons will always attack first. Complex actions - such as moving 30 feet, than attacking four times, then casting a cantrip with a bonus action - would be broke down into smaller components - maybe you can move 10 feet before your opponent shoots you with an arrow, for example.
But... this would be TOO complicated, right?
Well, we will see in the next post.
(Thanks Telecanter for the silhouettes).