So, not perhaps exactly what they want, but something sort-of close.
Something as close as possible that won't mess with the concepts of the other players nor the DM's campaign, yes.
The same can be said for both roll-and-rearrange and fixed-array.
To a lesser degree, yes, and I thought I'd been fairly clear in that. Arrays can let you build the character you want, as long as it isn't more extreme or more 'all around' than that array. Roll-and-arrange methods give you a similar level of customization, you can choose where to but high and low stats, but not the high-low spread.
The only method that has a real chance of messing up a concept is roll-in-order.
It also has the best chance of inspiring you to build to a concept you'd've never thought of otherwise.
This one doesn't make sense. How does stat generation method have anything to do with players competing to play the same 'role' (or class) in the party?
With a random (or freeform) method, if two players do go for concepts that require similar stat priorities, one can be flat-out better at that 'role' (or class) than the other, undermining his concept. With an array or point-buy, they'll have to settle for ties, or find some other nuances to differentiate themselves, there's no risk that one will just overshadow the other.
I will go there every single time.
Then logic will not go with you.
If you're intent is - as mine is - to try and reflect a real-ish game world population with people in it who are not all the same, that variability will also extend to played characters...
allowing the PCs to (on average) be a cut above by giving them 4d6k3 or even 5d6k3 instead of the general population's 3d6.
I don't see that as quite the same variability, but OK. (And, no, you didn't "go there.")
Rolling - with or without rearranging - reflects this randomness nicely
Rolling is randomness, yes, but there's no difference between the world painted by randomness, and one where the exact same results have been arrived at arbitrarily. For the PCs, a much smaller sample size, OTOH, random generation can give very different results.
something that only just occurred to me while typing this (though maybe old news to everyone else): if 3d6 gives what seems like too loose a bell curve for either or both of the PCs and the general population, a tighter - i.e. much lower chance of extremes - 3-18 bell curve can be achieved via rolling 5d4-2. Maybe this would work better for rolling up commoners?
Yep, that'd compress it a bit. Don't know why I'd never thought of it - I'd seen 4d4, and even 6d3, for that purpose before.