To a point, yes.
If one went nuts, sure. But the game didn't break if your party had no* or nearly-no magic, nor did it break if your party had gone through a few classic modules and scooped all the rather-abundant loot from those. There was a wide "what/ how many magic items does the party have?" window within which the game worked fine; significantly wider than 3e I think.
Magic items were also much more easy come easy go in 1e, given that some bad luck with AoE saves could strip you clean in a hurry. 3e largely did away with this (I think if you rolled a nat. 1 vs AoE then one of your items had to save, or something like that), and 4e and 5e have no item destruction that I can recall.
* - unless the DM was cruel and threw in opponents that required magic weapons to hit.
I really don't think it required DMs being "cruel." Which is sort of the point. Some things expected magic items. Others didn't. Cruelty, ignorance, or simply lack of forethought can cause a "essentially no magic items" game to run aground on such a thing.
I'd quibble about the volatility piece (see below) but otherwise not a bad summary.
Not bad until the very last word - did you mean 2e? 3e doesn't follow this pattern in that it's quite reliably lethal, fairly gritty, and does rely on a certain amount of bookkeeping etc. (though you're recording different things than in 1e).
I meant 3e, but 2e isn't that far off either. I just find that, because 2e was
pretty much backwards-compatible with 1e, it has far too much baked-in stuff for the "Gygaxian" experience. 3e was designed that way from the ground up; 2e was that way mostly because of the changing culture-of-play. (There are more specifics here, but I'm trying for more brevity.)
I disagree with the level of volatility you suggest in both 1e and 3e, if in "character status change" you include non-death bad things. Both 1e and 3e (sort of) had level drain, poison, and a host of other effects that 5e either lumps under hit point damage or eschews completely; and in this way I'd say both are quite volatile. The one difference with 5e (and 4e?) is that most of those effects can be shrugged off much faster than in 3e or earlier.
But those statuses stick to you. They have to be removed by a spell, generally speaking, or occasionally a potion or whatever. The status changes...once.
Things changing both rapidly and repeatedly is what I refer to as "volatility." 3e status doesn't really change repeatedly, particularly as you get into the higher levels, and the early levels (where they actually did do balance testing) are still pretty deadly, but both monsters and PCs don't have the resources yet for rapid change. Once they do, the power level has ratcheted up enough that it's, as mentioned, more 'rocket tag" than "volatility."
To use a
very loose analogy, 1e (and to a lesser extent 2e, mostly due to culture-of-play as mentioned) is like a firefight between two sides where each side has a small number of very powerful grenades, and the ability to (attempt to) strategically predict where enemy soldiers will be; whoever
prepares best wins. 3e starts out as a firefight where both sides have relatively ordinary guns with low ammo capacity, so things change relatively slowly, and grows until both sides have rapid-fire, high-capacity bazookas; whoever has initiative wins.
5e tries to thread the needle, reducing the top-end power but still giving out some rocket-propelled grenades, but also reducing the ability to predict the enemy first, but also leaving big gaps in defenses that can be exploited, so there's still
elements of both sides of things.
Games like 4e, PF2e, and 13th Age, on the other hand, lean into a style of play where actual character
death is pretty rare (not impossible; I've seen two deaths before 4th level in a 4e campaign), but the status of both individual players and the battle overall can swing
wildly from "oh crap, this is bad" to "WE ARE THE KINGS OF COMBAT" to "bloody hell this isn't good" over the course of literally a single round, and where each individual character may go from top form, to barely surviving/bleeding out, to back in the action over the same span of time. By comparison, both "Gygaxian" and "Lancian" experiences are quite low in volatility--because once the initial salvo is done, you either already know the winner, or you're in for a slow slog. The one area of volatility 5e actually does have is often reviled: so-called "whack-a-mole" healing. Folks want statuses that linger, that keep you down for the count, not ones that quickly change from round to round or even turn to turn.
The difference between actual trench warfare (where progress was either lightning fast because the defensive lines collapsed completely, or glacially slow because they held strong) and a high-stakes street fight. Both have ambiguity, both have tension, but the former (generally) locks up all the tension in the first round or two, while the latter mostly spreads the tension out across 4+ rounds. Both are serious combat, but one is (generally) with an eye toward the combat
theater, while the other is more with an eye to the combat
field. (Hey, there's a non-judgmental alternative to "war vs. sport"!)
Also, I'd say 3e is mid-to-high lethality all the way through, right from 1st level.
I think culture-of-play may be involved here, too, but RAW you're probably right. Many folks used the "max HP at first level," and IIRC that was officially the rules of PF1e. That might be where my description is rooted (since I actually have more experience with PF1e than actual 3e/3.5e now.) If you stuck to rolled HP even at first level, then yeah, 3e could be quite deadly for the first 1-2 levels, and then got somewhat less so for levels 3-6ish, and then the rocket tag started to creep in, inflating the numbers again.
