PCs need three good stats: one ability score for each NAD. That's assumed for monster accuracy.
Monsters gain a +1 to defences and attacks at each level. They scale identically. PCs gain a +1 bonus to defences and attacks every other level, with the gap every second level filled by magic items and stat boosts. The defences of a PC increases at the same rate as their attacks which should both keep pace with monsters' attacks and defences.
PCs also get feats (monsters don't) and a lot more powers than any monster. I don't believe the to hit rate falling behind was actually a mistake in the maths at all.
However, as you say, PCs can only boost two stats each level. The fact that one NAD lags behind (by as much as 3 points) is a flaw in the execution of math.
Other than that as soon as it exceeds +2 (i.e. in Epic) you get access to an untyped feat that can add 4 to a NAD.
Yes: they deal damage. On average, they deal identical amounts of damage each Encounter.
The how is irrelevant and only the execution varies.
To recap, the claim is that a Sorcerer and Ranger deal identical amounts of damage per encounter because they are both Strikers. This is false. And it's more obviously shown to be false by, for example the PHB Warlock and the PHB Ranger. With the ranger dealing a lot more damage than the warlock, despite both being Strikers. The Warlock on the other hand being a secondary controller, something you apparently don't think exists in the PHB.
Your claim is both conceptually and empirically wrong.
Your first point here is the HOW 3e optimized. Which is irrelevant. 4e does not replicate the how, it replicates the effect: characters dedicated to a single purpose.
This is neither true for optimised 3.X nor for optimised 4E. An optimised 3E character is a Tier 1 caster and can do almost literally
anything. An optimised 4E character is generally very broadly competent (the 4E skill system being flexible) and can cover slack. You appear to be confusing DPR Challenges and the like with in play optimisation.
Your second point brings up a subtle change in 4e class design, the idea of a secondary role. This was introduced after launch, some time before the PHB2 where each class has a primary role but their choice of subclass allows them to dabble in an aspect of another role.
None of this is true either.
First, classes in the PHB have subclasses. The most obvious one is the Warlock with Fey Pact, Infernal Pact, and Star Pact being subclasses that handle things very differently. All classes in the PHB have subclasses.
Second, there is a deliberate correlation between power source and role that's especially evident in the PHB. All martial characters are secondary strikers (meaning that the Ranger is a double striker and so the most single target damaging class in the game). All divine characters are secondary leaders (with the Cleric doubling up on the leadership while the Warlord does more damage as it's a secondary striker). All arcane characters are secondary controllers, which is why the Warlock is superb at handing out awkward choices. And all Primal characters are secondary defenders - very tough and the classes most likely to throw around Spirit Companions or shrug off conditions.
This was all there right in the PHB.
With system master and more options you *can* build a character to be good at multiple role, but this was not the intent of the game system. And a warlord PC designed to be a tank or DPR will still always be able to act as a leader. A skilled player can always build a character that goes against the intended design of the class/system, but this does not mean the intended design does not exist.
The intended design just isn't what you think it is. You can not play a member of that class without getting things out of that class/role. But how much you choose to focus on it is entirely up to you. A fighter built for damage can outdamage a warlock built for control. For that matter I've played a warlock that was regularly being outdamaged by the party mage (evoker/pyromancer). But did that mean I was unhappy? Not at all. My feypact warlock (officially a striker) was the one giving the DM fits and refusing to let the monsters do their thing. Sometimes by charging and hitting the enemy over the head with his staff to get the slide to push them off whatever ledge they were on. (I got a lot of weird looks when I tried that little stunt in the second round of the first encounter I played with that group). In short my warlock was for all practical purposes a controller, handing out blindness, to hit debuffs, and immobilising foes.
Yes but every single monster table you rolled on did not produce a fair encounter. Many games at the time had weak, moderate, and too powerful encounters. There was much more an expectation the the encounters were designed to fit the setting in a natural way and far less about a "fair" encounter. I'm not saying there was zero. I'm just saying that this obsession with balanced encounters became far more significant in 3e with CR than it ever was prior.
Nowhere in the rules to 3E or in the rules to 4E does it say that encounters must be fair in any way, shape, or form. This is a common misconception. What balanced mechanics do is tell the DM when the encounter is unfair.
That said, there was a shift towards fair encounters starting in 3.0. This happened when the Forge of Fury, entirely in line with the guidance, dropped a Roper into the basement. And there were howls of outrage from players getting TPK'd by that thing. (I've played the Forge of Fury - we decided that the Roper was not something we wanted to tangle with).