That's certainly your prerogative. But it is also incontrovertible fact that the CR system was not designed so that every single encounter could have an EL equal to the party's average level. Those using the tool for that, or anything remotely resembling that, are explicitly not using the tool in the way it was meant to be used.
How is it a fact that the CR system was not designed for that reason? The DMG actually tells you the percentage of EL you should use against a party in an average adventure. The numbers escape me right now, but it was something like 50% should be EL=APL, 30% should be EL=APL+1, 15% should be APL+2 and 5% should be APL+3 or higher.
It was the section of the DMG that we based he adventure creation rules for Living Greyhawk off of. We actually had a mandate from HQ(WOTC themselves) that monsters had to be level appropriate and average out to the pattern described in the DMG since that was the "standard" 3e experience and LG was trying to give the D&D experience the way that WOTC intended it.
You can use whatever monsters you want, of course, level appropriate or not. But it was certainly the intention of the rules that monsters were always appropriate(that's why every published adventure from WOTC had only level appropriate monsters).
It's also impossible unless you take away all player initiative in choosing and building their characters. (And you'd probably have to take away their ability to actually choose the actions they take in combat, too.)
That's not true. You do need to minimize the impact of those choices, however. A system that allowed you to spend 1 million points any way you liked amongst damage, defenses, roleplaying special abilities, attack rolls, stats, perks, and so on is the ultimate in player choice. But you are just as likely to end up with a character who has +499,999 to hit and damage and 1 hitpoint and 1 ac as you are the character with +0 to hit and damage because all their points are put into basketweaving.
This means that there is no way to tell if your enemy who has 1000 hitpoints and +1000 to hit is too powerful or too weak for starting level characters. You can only get approximately what people will put into their abilities. But because the numbers vary so much, your guess has almost no chance of being right,
On the other hand, if you can say "All 1st level monsters have a 16 AC and 20 hp. All players have +6 to hit and do 5 damage." then you can nail down precisely the percent chance of winning. But being that predictable would be a little too boring. So, you allow enough choice for it to be meaningful without allowing enough that it becomes completely unpredictable. if you allow players to choose options that vary their to hit and damage up and down 15% then you create a 35% difference between highest power and lowest power. Then you can add the ability to attack different defenses and then vary the defenses up or down 15% and you create more randomness and meaningful player choice. You add some tactical and situational modifiers and you add a little more.
But when you add them all together, the numbers are close enough that you can still predict the approximate difficulty of any given creature with a high degree of accuracy.
The best you will ever achieve in the real world is a ballpark estimate built on an assumed baseline. And 3E's CR system achieves that.
I disagree. 3e's system is mostly guessing. There is a chance that the CR 8 creature in any particular book might have an AC anywhere from 10 to 40. Same with all the rest of it's saving throws. So, when the designers looked at each creature and decided on a CR, it was mostly just guessing. They've admitted this themselves. It was a matter of "This creature has about as many hitpoints as this other CR 8, but it's attacks are significantly higher. We'll write in CR 9 and call it a day."
And it got closer to your theoretical "ideal" by taking away player choice in character builds.
Yep, it did sacrifice some player choice in character builds in order to get there. I don't have any problem with that at all. I started playing D&D in 2e where Wizards couldn't wield a sword, ever...simply because "They already got spells, you can't give them a sword as well". I think I can live with "choose amongst about 5000 different builds, about 4800 of which are good ideas for a character and completely balanced" vs "choose amongst 10 million different builds, only 2000 of them are worth playing, make any sense and fit within the narrow balance range that the game is designed for".
Plus, my experience with 3e eventually proved to me that not all choice is good choice. Mainly the 2nd campaign in a row that I ran where the PCs wiped 95% of the encounters I sent at them without even a small chance of anyone dying or losing. They all complained that they had no fun because there was no challenge, I had no fun because I felt like I was picking up dice and rolling for an hour and a half just to prove a forgone conclusion. Yes, this included the time I threw a EL 22 encounter against them while they were 16th level. Which, according to all estimates should have ended in a TPK of the party. Instead, the enemy got 3 actions, and all of them didn't actually hurt the party.