Well then, if the question is more "Can we avoid counting them and still be accurate?", then that makes things even easier! The answer is YES! Like I said, playtest it. You have not presented one bit of evidence that counting the ability scores actually works during playtesting. You have given a lot of theory and no playtesting proof to back it up.
Just look at the Party Level. ABILITY SCORES SHOULD NOT BE COUNTED. First off, let's forget the "all 18s" argument for a moment and replace it with a far more likely scenario, shall we?
In one Level 1 party, we have a Wizard with Str8, Dex 12, Con 15, Int 15, Wis12, Cha 8. By your system, this character would be CR 2 (Level 1, Ability Scores +1). In another Level 1 party, we have a wizard with Str 12, Dex 12, Con 15, Int 15, Wis 14, Cha 12. By your system, this character would be CR 3 (Level 1, Ability Scores +2). Do you see the problem yet? Both characters, in terms of party usefulness, and pretty much IDENTICAL! The Strength doesn't matter because this Wizard shouldn't be in melee in either case, the Wisdom only gives +1 to the Wizard's best save, and the Charisma does NOTHING. Yet you would attest that the second Wizard deserves to be counted as if he were A WHOLE LEVEL HIGHER.
You can use these scores at ANY level, and counting #2 as a level higher than #1 only gets more ridiculous the further up in level you go!
Now go to any normal player and ask them if they would like to play on a Level 3 party with a Level 2 Wizard with 8/12/15/15/12/8 (which would make him CR 3 now) or if they would rather have a Level 1 Wizard with 12/12/15/15/14/12 (the original CR 3). You attest these characters would be equal, but I'm willing to bet that any player who is paying attention will pick Wizard #1 because the level is NOT worth a +4 to Strength, +2 to Wisdom, and +4 to Charisma. Do you see the problem now?
You are trying to count things that simply should not be counted! Charisma is USELESS to practically half of ALL the Core Classes! Intelligence is also a score people sacrifice in most cases. Dexterity is easy to sacrifice if one plans to wear Full Plate most of his or her career. The ONLY score that is ALWAYS useful is Constitution. I know this because I am also a player, not just a DM. I KNOW.
Look, I never said, at first, not to count scores at all. I said not to count the standard array, or yuor basic "rolls". I said you SHOULD count monster "racial ability score bonuses" such as the ogre's Strength +10, Dex -2, Con +4, Int -4, Cha -4. You said it had to be "all or nothing", though, and you're wrong. There is the gray area where you ONLY count things "above and beyond" the standard array. I don't see why you have a problem with doing so, to be honest.
How about the rest of you? Do you think it's "all or nothing" or do you think that we can NOT count standard array ability scores while counting any racial ability score modifiers as I attested? I only said "don't count them at all" because it CAN still work if you don't overrate everything else.
So how about it? I think I have clearly demonstrated the facts of the matter. You DON'T have to count "all or nothing". Just figure out racial ability modifiers and COUNT ONLY THOSE. Humans get none and have no modifier. Elves get +2/-2, so they have no modifier. Ogres have +10/-2/+4/-4/-4, and thus get +0.4 CR. Heck, if you do it this way, a monster's CR can actually be used AS ITS ECL as well! That means you NEVER have to calculate ability score modifiers more than once, and that time would be for the base creature only!
See what I'm saying? Stop going to extremes and count the stuff that matters. There is no reason to count ability scores for standard PCs! So to answer the question, "Can we avoid counting them and still be accurate?", I have shown the answer to be YES. Playtesting supports what I say. I should know, I've BEEN playtesting these theories, unlike everybody else here who just keeps throwing out numbers and formulas. The playtesting supports what I have said. The playtesting is what shows the truth, not some formula.
What say you?