There is a big difference between chucking completely hopeless characters and rolling sets of 4d6 until you get overall higher stats. In the former case you are rolling and accepting what you get, but you might roll a new set if you got like three 6s and nothing over 12 (definitions of hopeless vary though).
In actual practice, I'm not sure there is. Keep in mind that definitions of 'overall higher stats' also vary, and definitions of hopeless will depend on those definitions. A functional definition of hopeful in 1e might be: "At least 1 16 and doesn't have a 5 or less in a conflicting category (for example 16 wisdom and if a 5 or less, then in dexterity) OR at least 2 15's in base class prime requisites (not charisma, in other words) and no 5's or less, at least 8 intelligence and at least 7 dexterity, OR qualifies for Ranger (2 14's and 2 13's and no 5's or less)." So hopeless might be deemed everything else. But another group may have different standards.
The important point is that everyone actually wants to be above the minimum standard, and preferably above them by a good deal. So take the case of a group that is happy with 4d6 drop 3, but also agrees that truly hopeless characters can be rerolled. And, look at the list of example ability scores generated by 4d6 drop 3. Even if the group doesn't do point buy, lets evaluate them as point buy with the idea that average stats are like 28 point buy. The first thing you note is that most sets end up being above 28 point, and therefore satisfy the players desires and expectations to be above average. A few are really above 28 point buy by a wide margin. However, there are a smattering of results where the system generated 9 point buy, 15 point buy, 12 point buy, 18 point buy and so forth. So imagine that happens. Well, SURELY everyone at the table will concede that's just a fluke, a hopeless character, and should be rerolled.
As soon as that happens, you've thrown randomness basically out of the equation. Imagine the similar situation in game where you throw a dice, it's a remarkably low rare result, and you say, "Well gee, that's not supposed happen. I'll just reroll the dice." Once the game starts that is called 'fudging' or 'cheating' depending on the demeanor of the table. What it really means is, "I had a result in mind. This wasn't it. But instead of actually admitting to myself that I'm choosing the results, I'm going to just reroll the results... until I get the result I was going for all a long." For some reason emotionally, for irrational creatures like humans, this lets them mentally believe that they aren't actually choosing the result. But that doesn't mean that this emotional conviction is in any way rational.
Once you grant that the player can reroll until he gets a non-hopeless character, look at that table of results again. By and large that first reroll is going to produce a 'correct' result. A few players may get a disappointing result just below 28 point buy, but there are lots of oppurtunities to 'win' once we throw out all the losers. And observe also what that is doing to the average result. If 4d6 take the best three is on average 28 points in point buy terms, 4d6 take the best three and keep rolling until you get a 'non-hopeless' result is in practice something like 36 point buy. Because the standard deviation is huge, so once you throw out the bottom 20% or so of scores, the remaining scores are really good indeed.
That doesnt ean your using 4d6 to somehow game a point buy you were never employing in the first place.
No, of course. I'm not claiming that the players had some knowledge of point buy to compare it too. I'm just using that as a means of measuring just how good, or not good, the various rolls are. I'm just showing just how wide the range of characters real randomness would produce if it was actually employed in earnest - which I'm asserting it almost never actually is.
Worse for me though was the fact that this illusionism around randomness meant that the bar on what was hopeless was being continually raised, particularly as people began to figure out what they actually needed to have the best shot of a highly successful career with a character. When we were using 3d6 straight up, that was a pretty low standard. At least not mostly scores lower than 11 was enough, which should have clued us in right away that our definition of hopeless was already 'anything below the average expectation of the method'. However, those characters tended to have short lives compared to the few lucky ones, and most people were - if not exactly cheating - working around the rules any way. So we went to 4d6 and the standards of what was playable went up, and conversely what was hopeless went down. In practice, it became 'not mostly scores lower than 13'. 12, 12, 11, 11, 9, 7 which might have been considered playable previously, gradually became understood to be hopeless. And I discovered that, I really couldn't make people play what they didn't want to play. So scores got better, but the percentage of 'do overs' - via some methodology - didn't decrease. And as I understood the math better, my ability to see why 13, 13, 13, 13, 13, 13 wasn't actually a good result, but a bland character that would always be inferior to his peers lagging in XP and with no reliable abilities, my understanding of what a good character for the system looked like evolved. I began to realize that guy with a 7 and two 8's wasn't actually paying much of a penalty if he had a 17 and a 15, and making him play it wasn't really a hardship nor was choosing to play it being really hard core.