Yes, 4d6 does often result in higher overall stats; but it doesn't necessarily increase the power level of the character. 4d6 has a tendency of achieving those higher overall stats by increasing the value of tertiary stats and/or increasing the proportion of odd stats; both inflate the equivalent point buy without increasing the actual power level of the character. 4d6 also makes an 18 ability much harder to come by than a point buy system does.
That's only true if you run 4d6 drop the lowest straight up (which I did). However, the default method 1 is 4d6 drop the lowest and
rearrange to taste. Most of your objections in practice don't actually follow. In 3e, even boosting tertiary stats offers major advantages. A fighter might could get buy without high dexterity or wisdom, but he certainly wouldn't object to them so having an extra high 3rd best or 4th best score or having no low scores in anything is certainly an advantage. Odd stats don't lead to immediate advantage at low level, but can be easily bought up at higher level to significant advantage. In fact, there is one school of thought that says that for certain classes don't pay for the even number which generally has high cost. Instead, start odd and use the point savings to boost a tertiary stat by 2-4 points and then boost to the even number at 4th level. And certainly in 1e with its less smooth adjustments, there was a huge advantage in a 15 over a 14 and 17 over a 16.
And while 4d6 does make an starting 18 ability somewhat harder to rely on, generally in point buy systems buying that 18 requires gimping all the rest of your stats. With 4d6, if you luck out and roll the 18, all the rest of your stats will likely be what they would be otherwise. You get that huge point boost for free.
Your argument that 4d6 in general didn't lead to large advantages relative to other players is more applicable to 1e, where a 8 in anything but your prime requisite was not significantly worse than 14 in most cases and you often pay no relevant penalty for it over the course of your career. So for example, a 1e centered point buy might well make it cost almost nothing to boost an 8 to an 11 and little to boost and 8 to 12 or 13. Thus a player with the stats of 16, 15, 8, 8, 8, 8 isn't in 1e really that much disadvantaged over the one with 16, 15, 13, 12, 11, 11 even though by 3e centered point buy systems we might say the second scores cost much more to buy.
However, I think we've pretty definitively demonstrated that played straight up with no rerolls, 4d6 drop the lowest produces a range of 1e starting characters between hopeless commoners and nascent demigods even over small sample sets. And once you add a table rule that lets you "reroll hopeless characters until you get a good result", the average point buy in 3e terms becomes quite high - generally above that of any standard point buy. Arguably, even if this was balanced for 1e's expectations of starting character ability, it's not balanced for 3e's EL/CR expectations which assumes that characters have something like an elite stat array to begin with. And even to the extent that you can deal with that, it's certainly not balanced between the players themselves or ensuring equal access to gameplay.
However, for practical purposes, most 1e groups found some way of dealing with this by working around the randomness to get a end result similar to "set your own ability scores", so that many groups could say, "I've never seen a fighter without 18+ strength." I didn't run my own table that way, but I certainly did play with DMs who found that tolerating that sort of thing was better in the long run that trying to hold players to the results of the random methodologies.
Had I to go back to random method, I'd probably use some variation of Method III and perhaps adjust the number of rolls in each group (probably down to 5 rolls per group). Method III produces rather OP characters compared to even Method I, but basically never requires a "hopeless character" rule (which means in practice it isn't that far from Method I + rerolls) and produces must more consistently playable characters concentrated around a small range of power levels. I think you could use Method III without the social illusionism and hypocrisy I've seen around Method I or even Method V.
