That is why, when I play, I prefer to have the DM roll my stats for me and just tell me what they are.
As a powergamer, it's more important to me to be on an even playing field with the other players. As such, I hate hate hate rolling stats. If somebody rolls significantly better than me from pure chance, that bothers me.
You are right, but the flow chart from "Yes" looks like the following:
2) Are the results above point buy. If your answer is "Yes", stop, otherwise go to 3.
3) Did the player argue successfully that he had an unfairly bad roll and should be allowed to reroll? Or be allowed to reroll 1's. Or any other sort of reroll. If so, return to 2, otherwise 4.
4) The player now declares the character unplayable and the character is committing suicide or being retired. Return to step 1.
If I got a nickel any time that happened and paid a dollar any time it didn't, I'd still be rich.
I've been playing 30+ years. Rolling stats is just DM approved cheating.
These posts highlight why as soon as it became a clearly viable option to do so (5th edition with its ability score cap and relatively smaller difference between "good enough" modifiers and "best" modifiers), I changed my ability score generation method to "Just get scores you will be happy to play with, I don't care how - even if you choose them arbitrarily, copy another player's scores, or show up with straight 18s before racial modifiers."
That mildly off-topic-ness aside; In the past, I've always let it be a choice of the group by way of a vote as to how ability scores should be generated - I've even seen the same group change what they voted for from one campaign to the next, sometimes wanting point-buy, sometimes wanting super-powerful characters like 5d6, reroll ones, keep 3, 3 full sets of scores and pick the best, and occasionally even wanting the "ultra hard mode" of 3d6 rolled in order and you actually have to try to keep the character in the campaign long-term.
Dice-generated scores tend to, in my experience, be higher than point buy because they are typically a rolling method that makes higher scores more likely than lower scores, and that along with detaching the height of one score from the height of others (meaning rolling a 15+ on one score doesn't affect your ability to have a 15+ in another score, where point buy is designed so that any "peaks" cause "valleys") naturally results in scores that are higher on average.
As for why it seems that if you don't watch a player roll scores they manage to consistently get highly improbable score sets - that's because the player feels like they "need" those scores for some reason. It can be because the DM creates challenges the player feels are more difficult than they'd like so the player is trying to get the odds they would prefer, it can be that the player is just curious how such a character would be to play because they've never played such a character before, or it can be some other reason that doesn't even necessarily make any logical sense. But there is always a reason for the "cheating" and it therefore can always be prevented by discovering and removing that reason.
Of course, the only proof I have of that is the anecdotal evidence that in my current group which are allowed to generate ability scores however they should desire, no one has chosen to get even higher scores than they've previously had - they are all actually starting to trend more towards the only player with strong preference for ability generation method, and rolling 4d6 drop lowest, one set only (though she keeps her scores in the order rolled, while everyone else rearranges the scores they roll), though a large part of that trend is "I'll just use what she rolled."
