Generally, when I want randomness (and I don’t always), yes, the possibility of some characters being significantly better or worse than others is part of the point. But, it should be noted, the appeal is to be able to get significantly better or worse stats than your own past characters. Different players getting characters with significantly better or worse stats than other players’ characters in the same party is not specifically desirable.
I think it really can’t be over-emphasized how important high lethality is to this type of play.
Or high turnover in other ways, and even moderate lethality is enough IME.
Also, randomized treasure, and potentially randomized dungeons are huge boons to this type of play. The point is to make the game into sort of a roguelike.
Yes! At last, someone finally gets it!
The dungeons and treasure don't have to be fully randomized. That they are designed/placed without regard to which specific characters will be involved is enough. All you need is a vague idea of what their average level will be, and in some editions you can even miss this by a few and still have a playable fun dungeon.
And the joy of playing a roguelike is when that one character finally does break through and stick. Same in D&D: the original party starts with six characters of whom one might go on to become a superstar, a couple of others might hang on for a few adventures, and the rest will fall. Those who fall are replaced, and sometimes the replacements become the superstars in time. There's just no way to know.
I far prefer this type of game to one where a character's place is already reserved in the Hall of Heroes before it even enters play.
You’re not lovingly crafting the perfect character to play out their story over the course of a lengthy campaign. You’re generating an avatar for your next run into the dungeon, with the goal of making it as far as you can before the run eventually, inevitably, ends.
Kind of a mix, actually - you could be lovingly creating the perfect character, but in full knowledge that its career might (or might not) be very short.
More importantly, what happens is the focus of play becomes playing out the story of the (ever-evolving) party rather than that of any one character. In the later stages of the campaign, once the character lineup has stabilized some (IME this happens at about the point where characters become rich enough to afford to have NPCs cast revival spells), then sometimes character stories become more front-and-center.
Then you go again and try to get a little further. Less Baldur’s Gate III, more Binding of Isaac. In that context, if you roll up really low stats, that’s a bummer, but the worst that happens is the character sucks for a few sessions before they die, and you get another shot at a new character with better stats. If you roll up really high stats, that’s exciting, but it’s far from a guarantee of survival.
The last point is very relevant. High starting stats are no guarantee of long-term survival, and I've run numbers in my own games that back this up. They showed that as the average starting stats went higher (divided into brackets) there was a tiny and very inconsistent increase in career length; I'm not statistician enough to know whether this increase would even count as "statistically significant" but I suspect it would not.
Far, far more important was to survive your first two adventures regardless of what level the game is currently at. Most characters, if they're going to permanently die off, do it fairly quickly.