5e is a FINE update of 2e, basically. If you take 2e's concept space and reimplement based on the experience of 3e, then you have basically 5e.
I think 4e is a necessary developmental step between 3E and 5e. Probably the most striking differences between the two games are that (i) 5e has a two-rest recovery economy, and (ii) spells in 5e use a fixed rather than a X/level damage expression. And (i) and (ii) are inter-related in that, together with the
6-8 encounters with 2 short rests per day guideline, characters should be roughly comparable in their contribution regardless of class.
These are all direct legacies of 4e, although (unlike 5e and 13th Age) 4e doesn't need an X encounters per day guideline prior to Essentials, because everyone's on the same schedule.
4e also trialled bounded accuracy, aiming for a more-or-less steady 65% hit rate for players. 5e largely keeps this, though it reduces the hit rate for monsters to something less than 4e, though still more than AD&D.
I wouldn't quite say that 5e is Essentials with the serial number filed off and a new coat of paint - but I think it's closer to that than is sometimes recognised.
4e tried to address perennial problems with D&D, but I don't see how it tried to become a thought-leader in the industry. It did things that were new-to-D&D, maybe, but nothing innovative as far as the broader industry was concerned.
Skill challenges are new in the technical sense - a players-make-all-the-action-declarations closed scene resolution mechanic. (HeroWars/Quest, for instance, which has a very mechanic of this sort, relies to a significant extent on opposed checks.)
Whether this is a
good innovation is a trickier thing: with no action declarations from the GM, it can be easy for the resolution to degenerate into the notorious "dice rolling exercise"; but with no need for the GM to correlate the events on his/her side to actual action declarations or die rolls, and with the DC setting mostly handled by the chart, it does free the GM up to go nuts with the genre appropriate fiction.
I also think that solo monsters are an innovation. The BW rulebooks often have a "further reading" section that includes other RPGs. In the BW Adventure Burner (which is a bit like a GM's guide), the further reading includes 4e. I don't think it's a coincidence that this book also has advice on how to handle action economy issues between several PCs and a single "big bad" type. 4e tackles this perennial issue in reconciling RPG mechanics (especially combat mechanics) with dramatic conventions head on.
(And 5e's Legendary Actions clearly owe a big debt to this 4e work, although they are even
more "dissociated"!)
A final 4e innovation, in my view, is reconciling non-sim Gygax-style AC-and-hp combat resolution with high-resolution, almost "gritty" tactical combat action (positioning, 6-second rounds, etc). 3E had elements of each, but (at least in my view) suffered from having too much "grit" in its hp (implausible flirting with simulationism, or "pseudo-simulation as veneer" eg +30 natural armour bonuses); and suffered from not actually putting the tactical detail to work (eg forced movement too hard to achieve; full action issues; etc).
4e is able to deliver a tactical overhead and intricacy comparable to (say) Rolemaster, but within a completely different, Gygaxian "heroic fantasy" paradigm. That's an innovation.
Overall, I would sum these up as borrowing from, and adapting, "indie-"style/Euro-style design, and showing that you can use it to build a fantasy RPG that will be a playable, D&D-style game. And that will deliver heroic fantasy without needing to go as abstract and free-descriptor as (say) HeroQuest revised, but without needing to punt everything to GM fiat.
I think it's a real achievement, and something new in RPGing, even if - as it turned out - not to everyone's taste.
