Take a second example. A basic system that all players must use: Character generation.
System 1 in AD&D is 4d6 drop the lowest, arrange to taste. Ok, fine. Now, take two hypothetical groups. The first one gets average results - a couple of 15's between the characters, nothing below 9, most of the rolls between 10 and 14. Group B gets a lot luckier. Each PC has one 18 and one 16 and the rest of the rolls tail off from there.
Now, the power disparity between these two groups is pretty significant. In a system designed for balance, how can you get two groups with such a massive disparity of power?
I'm picking this example because it's the easiest demonstration of the false set of principles you're working from.
Let's take a simple game: Shuffle a deck of 52 cards. Each player draws one. High card wins.
This is game is, prime facie, balanced: Assuming proper randomization of the cards, everyone has an equal chance to win the game.
Player 1 draws a Queen. Player 2 draws a Three.
This is madness! In a game designed for balance, how can you get two players with such a massive disparity in power? The Queen completely crushes the Three!
Balance is about having an even playing field. The paradigm shift, howver, is about where the even playing field starts and ends:
(1) AD&D1 says that the even playing field starts before character creation even begins. And, as far as character power is concerned, ends as soon as your first stat is rolled.
(2) You're saying that the playing field should be even after character creation ends. In fact, you're going even further in your other examples: The playing field should remain even forever.
Take this far enough and you end up with, "The playing field should be even forever, no matter what choices the players make." (Which is basically the ideal the designers of 4th Edition say they were aiming for.)
You may not see that as a problem, so let's take a moment and push the paradigm even further: The playing field should be even at all moments of the game. So even after 20 rounds of combat, the PCs and their opponents should still be exactly evenly matched.
AD&D1 was designed for balance. It just wasn't designed for balance using the paradigms you (apparently) prefer.
Sadly, I think one of the features now called balance is an equal ability to affect the game at any given time.
That's so not true.
4E certainly reduces the variance in how much you can affect the situation
It's not true because it's certainly true? Intriguing debate tactic.