I'm going to let others debate which editions have good CR or party level predictability or if DMG alternate rest recharge rules are a fallacy, I don't really see how those relate to the OP. But here I think I see something interesting where I have some observations to make, specifically towards new people adopting the game --
Putting down my own thoughts before I read other responses that might influence them...
I think "special" is a semi-loaded word.
I don't think any other edition of the game that we've seen previously would have performed so well in the broad marketplace. I think 2e and earlier the designs are kind of clunky, as you'd expect of games from early in the invention of game design. 3e and 4e put so much force to design that they come up a bit too crunch/complicated to grab so many folks who aren't already dedicated to the game.
Mind you, that doesn't make 5e a better game than others in some overall sense - that's the loaded nature of "special". 5e gets people to play, and that is awesome. It is not the only awesome thing a game can do, though.
2e and earlier certainly had a bunch of weirdness. Most or all all had a bunch of arcane unclear parts and obtuse wording and a lot of what looks like complexity in search of meaning (ex. why am I reading along an attribute table row which has different methods of resolving bending bars/lifting gates and opening stuck doors?). This is the kind of thing that, while not prohibitive to most people of most levels of ability, can easily be inhibitive -- as in, this looks like a whole lot of thrashing about without an obvious payoff (especially if you're also starting out at level one when things are most lethal and you're learning by trial and
errordeath that you shouldn't touch the green slime, etc.) and a whole bunch of people who were exposed to the game just didn't get over the hump that moved things from burden to fun and thus didn't take it up/stick with it. That was my experience growing up in the TSR-era -- there were a lot of friends, acquaintances, and schoolmates who ought to have fit the target interest group who tried it, didn't enjoy it, and stopped playing.
BX and the BEC portions of BECMI (as we've seen in recent threads, the part people actually bought) are, arguably, relatively simple. They still have different xp to level for each class, the saving throw table, etc., but the fundamental play loop was relatively straightforward attributes; combat using a chart, but once you add attribute modifiers and magic item pluses to the attack matrix, then things only change when you level or switch weapons; a more straightforward initiative system, and so on. And those were the ones that I saw the most uptake (at least briefly) from these potential players. Case in point, one kid in my main group had a sister who joined for a summer in the middle school era -- We put the modified attack matrixes on the sheets so there was only one place she had to look for combat ability, explained spell memorization, and she could play the character of anyone who couldn't make it that day. However, even those two version are married to a bunch of notions like Tolkien-like races* and their role-restrictions, or just the whole low-level system predicated on dungeon crawling through deathtraps for loot**.
*At a time when we all knew of the Hobbit and Lord of the Rings, but it was a long time before the Jackson movies and we weren't clear on why they took precedence over the Chronicles of Prydain and thus didn't know why dwarves shouldn't be able to cast magic like Doli
**Which is fine, if that's what you already wanted to be doing. To someone still on the fence about D&D in the first place, this was a second sell you had to make at the same time.
Then WotC got TSR, and... well, in some ways the games got simplified and some cruft was removed. Some form of central general resolution mechanic was included, the games acknowledged that you might not want to be dungeon-delving at any given level. At the same time, there are feats. There is multi-classing*. Your attributes change throughout the game. There is a notion of building your character out of parts that requires a level of commitment and investment. Your AC can change based on what you are facing. It's obvious people have strongly held and contradictory opinions about which of 3e, 4e, PF1, and Pf2 are most accessible and why, but for me,
all of them look like really good options for someone's
second RPG they ever learn (or at least one where there is a higher hurdle to get a potential gamer interested in getting past the learning curve, such that a better sell is needed). Certainly there are people like Darjr's son who started with 3e, but I'm guessing he had a bunch of like-minded friends already doing it (and if they didn't as well, that would be one less thing they would be doing together), and/or possibly some more experienced bigger kids/helpful adults such as the
Shadowrunners who helped Art Waring and his friends get into the game. At the very least, I suspect that there were a lot of kids like Darjr's son that didn't get past the 'why am I doing this/when is the fun bit?' stage and thus didn't stay with the game.
*not that there wasn't in TSR-era, but it was pretty well separated as a extraneous option you didn't have to learn if you didn't want to.
That, I think, is where 5e has helped, it is just enough step back towards BX/BECMI (minus saves vs wands/staffs/rods and forced aesthetics and quick succession low-level deaths) in specific types of simpleness that allow the casuals or lookyloos or potential recruits or however you want to look at it in the door and staying long enough to listen to the full elevator pitch, try for a bit (and have fun doing so), and stick it out. I think having that, now, in a post- "everyone has seen LotR, most people know what a Game of Thrones is, many watch anime, the MCU exists, it's hard to argue that nerd culture isn't mainstream culture" -era is something special and I think it has helped with the games' current rise well and above what Stranger Things and Critical Role and such have done for it. Is it unique/could there not have been another version which would have done similarly well? Certainly not. But I do think that there were specific parts of 5e that were right-place/right-time/right-application.