I feel like "allows optimization, still generalist-friendly" isn't too far off from describing 4e though. Everyone gets a half-level bonus to everything, which means "at-level" challenges hover around the same odds of success. The world is not keyed to specific level, however, so challenges that could not be overcome before (such as bluffing an angel or whatever) become possible, even (potentially) trivial. In fact, as I understand it, 5e's Proficiency bonus essentially acts as a slightly-flatter version of 4e's half-level bonus--it scales up at roughly the right levels for a half-as-fast growth with a slightly higher starting point (+2 instead of +0). Since this only applies to some things, rather than everything, one might even make the argument that 5e isn't quite as "generalist-friendly" as 4e, though the obvious rejoinder there is just that the numbers aren't supposed to get so high that an untrained rube couldn't at least possibly succeed. (The actual implementation of that, unfortunately, appears to vary.)
I've often remarked that there's two parts to each of 4E's roles (maybe more). Defending is being tough enough to take hits and discouraging enemies from hitting others. Striking is strong attacks and avoiding enemies attacks. Leading is aiding the attacks of others and restoring their condition or health. Controlling is attacking multiple enemies and preventing enemies from attacking effectively. So that'd be Tough, Threatening, Strong, Evasive, Supportive/Enhancing, Recuperative/Healing, Area/Wide, and Weakening.
To do something similar for exploration and social shouldn't be too hard. I'm not sure it's practical to separate exploration and social as different things while social skills are mainly related to two or three stats and exploration skills are mainly related to five. I'd combine them. So they'd be Scout, Expert, Sage, Athlete, Friend, Liar, Foe, Listener, Investigator. Probably more I'm missing. Does it make sense to separate the social and exploration abilities in classes? Does it make sense to balance them between classes?
I was discussing general design principles, and my 4E experience is limited to three sessions (because of DM issues), so I don't have much to say about 4E. About 5E: one implication of the flat curve you mention is that 5E is also friendly to parties with heterogenous levels. You could have a 20th level Gandalf, a 14th level Aragorn, an 11th level Boromir, and a couple of 1st through 3rd level Hobbits in the party, and they'd all be able to contribute meaningfully. If proficiency bonuses were massive (+1 per level) then Gandalf would dominate the whole party in every field of endeavor from social intercourse to engineering to mountain climbing. Systems with a "god stat" that allow super-generalists like this tend not to be very fun in my opinion, unless you are explicitly going for over-the-top James Bond-ism (GURPS: Black Ops).
Anyway, that's why I think it's an important feature of 5E that they consciously made the variance so high, and the d20 roll such an important component of any skill challenge. And from there it follows that even a Shadow Monk with a total bonus of -1 to Intelligence (Nature) can still look for poisonous herbs for his herbalism kit in the wilderness with some hope of success, if he thinks to do so. It may or may not be realistic, but it's definitely a distinctive feature of 5E play.
I would disagree slightly with the description of strikers above - for me it's strong attacks, and being able to pick and choose targets in some way, whether its ranged attacks, improved mobility, stealth, teleportation etc. Strikers tend to be relatively squishy with medium to low defenses, hit points and healing surges, so they make excellent targets for monsters, and benefit a lot from support from defenders, leaders and controllers. Strikers may have a few defensive powers, but by their own they tend to depend on a huge alpha strike to overwhelm the enemy, and their squishiness makes them vulnerable to counterattacks and they can shatter like glass cannons if taken by surprise. Which is the glaring weakness of all-striker parties i.e. they need the initiative and probably lose if they ever lose it.
The main issues to avoid are being good at too may things(e.g. Codzilla), or being good at too few things (the fighter trap). Different games vary hugely in adventure activities, so balancing across all pillars is going to be inexact at best. For instance, bards tend to be super good across the editions in very low combat, very high social campaigns, but in conventional adventuring vary hugely in effectiveness between the editions.
I think your example is...more than a little far-fetched. Even if we make all of the characters involved "normal" characters (that is, ones which follow the rules of character creation even if it means not doing everything Gandalf etc. could do), the level-1 Hobbits are going to have net bonuses to their best stuff (max stat+proficiency) of roughly +6, while Gandalf and Aragorn rock roughly +11. If he's an Evoker (reasonable, he makes fireworks) Gandalf can do more damage with a low-rolling cantrip than those Hobbits can do on a crit. And that has nothing on the Hobbits being at risk of immediate death if fighting anything above level 6 or so.
In certain narrowly specific ways, yes, this party "works" more than it would have. Most, but not all, foes can be hit by the hobbits with non-crit attacks, but many of them will still be in the 10-15% range. Most, but not all, enemies will not be guaranteed to hit the hobbits, but their odds of success will be in the 70%-or-higher range. Skill checks that Aragorn finds challenging (say, 40% odds of success) will be nearly impossible for the hobbits (roughly 10-20% with proficiency and a +3 stat; impossible, or nearly so, if lacking both). So...yeah, I don't think your example is especially great.
That sounds like a bad experience!
What sorts of changes did your GM make?
Even without mechanical changes, if the GM was running a lot of combat encounters with only a very small number of opponents, that would reduce the effectiveness of a fighter (who is good at controlling large crowds, marking them, etc) while enhancing the rogue and avenger (both single-target specialists).
Also, if the GM took a punitive approach to non-combat resolution (I think there is a bit of a D&D tradition along these lines, running through 2nd ed and 3E) that could have hurt your fighter too, who will tend to be better in non-combat with imaginative play and adjudication.
Ugh, yeah sounds like a DM issue. Avengers don't do "more damage" per hit than other strikers, or even a number of well-built defenders and leaders, depending, unless something really weird happens. Their thing is they *never miss.There was more, but i have since forgotten. The Avenger did 3-5 times more damage than I did in a single round of combat.
Probably the Blood Mage Wizard Paragon Path or pre-errata Blood Iron Weapon shenanigans. It was one of the few ways to get a good damage boost out of a single-classed Swordmage with a Wizard MC.Well minions/large crowds were generally wiped clean with the Swordmage Hybrid AoE powers. Something about he hurt himself and damage dealt was increased. I didnt audit the power, but he had the power whether ligitimately from the books or augmented/designed by the DMs.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.