We've always had a great deal of randomness in generation of things like previous professions, backgrounds, languages known (other than your own), etc.
That's the point. Just like many things in real life are based on luck.
Sorry for the delay; I forgot to get back to this.
So the main question I think has to be addressed to decide how you want to do it in your game, is where do you included choice, and why? Traditionally, you don't pick your ability scores, or you hit points, or the spells you learn on level up, but you do get to pick your race and class.
With just those variables, I think race stands out as an odd one to pick. If you
only got to pick your class, then there would be some consistency. Here is a random person you get, now make of them what you can. But why do you get to choose to be born an elf, but not necessarily a graceful one? It's a weird agency insertion point.
Flip side: if one wants to minimize the character-build aspect of the game, random is the way to go. That way you can't come to the table with everything planned out; you have to take what the dice give you and work with that, and develop the character through play rather than pre-play mechanics.
Yeah, I was trying to include that sort of play goal in my description of reasons for random generation, but I must not have been clear enough.
Except - and this is the key thing - people aren't equal. So why should the characters be?
I get nothing out of playing unequal characters, unless that's an explicitly presented and accepted part of the plan, and there is a
reason that works for me. So if I'm presented with a situation where a party of characters is going to have vastly different roles in a narrative focus, like the Fellowship of the Ring, then I might be interested. But if it's a game where the goal is to face challenges and grow in power, everyone not starting at the same level is a complete disincentive to my participation. I'm mostly referring to long-term play though. I'm game for just about anything for a one-shot lasting 4 or less sessions.
Curious here - what means of rolling did you use to achieve this?
I can't recall the precise system I used for the equal random generation (and the next time I'll improve it), but I can remember bits.
-I had a number that the raw random ability scores eventually needed to add up to. The stats were intended to be high for campaign-specific reasons, so I believe it was something like 80 or 82.
-We started with everyone rolling six ability scores. It was probably 4d6 drop lowest.
-After that, there was a cycle of rolling a d6 to target one of the ability scores, and then (I think) rolling another d6 to add or subtract from it, based on whether the ability score total was above or below the target total value.
Something like that. It was a little too messy, but I only needed it once and it generated some interesting results. The point buy option was a more typical 5e point buy, with a few more points. Because there is an increasing cost with point buy, and you can't efficiently get stats very low, the way it worked out was if you wanted to keep your stats pretty close to each other (hovering around 14), your ability scores could add up to a higher total than the random method.
But, the random method could let you start with higher values that you couldn't otherwise buy with point buy. This meant you wouldn't want to take one of the random values unless it was giving you a wide stat range, because you could otherwise do better buying stats. As I said, I consider it a success because I had people carefully consider it and take both options.
The motivation is, to some extent, reflect the reality that not everyone is created equal (or, better word, equivalent). Further, to gently promote the idea that D&D, at the end, is a game based on luck. If it wasn't, it wouldn't use dice.
The luck angle is an interesting idea. I'm sure there is some sort of deeper analysis that could go on here. The way I experience it, I want luck to mostly have a short-term effect, not a permanent one. Permanent effects are more desirable to me as the results of consistent choices over a long span of time. Sure, in the real world some bad luck can ruin your life, but I don't find that a particularly desirable thing to bring into my entertainment. And I'm the kind of player who's willing to go through a lot more of a "grueling" play experience than anyone else I play with, so that's saying something for me.
But again, it's all about knowing what the play goal is, and figuring out efficient systems to provide it, rather than fighting systems that are getting in the way.