The point I was making was that 'this method allows any player to play whatever they want' is simply not true. Not for point-buy. Not for rolling.
The point you were making it against was not literally anything, but anything within the parameters of the campaign. Making this point that you've fought so hard for, pointless.
The reality is the same as it was at the start:
Point buy gives you the maximum freedom to design the character you want, every time.
Array or random-and-arrange give you fewer degrees of freedom, you can choose how to distribute stats but not what they'll be. An array of 6 different numbers maximizes that freedom, while random might well deliver the same, it may also deliver two or more identical numbers (theoretically even 6, though it's unlikely), reducing the degree of freedom accordingly. It can also, for example, deliver a SAD array to a player wanting a MAD class or vice versa.
Random-in-order, of course, gives you the least ability to play the character you want. But, it has the corresponding advantage that it may spark an idea - you may get to play what you didn't even know you wanted.
For example I could see generating a list of all possible values you could get from a point buy system (including the ever-so-boring all 13's and a 12 if I remember correctly) and then rolling to see which value from the the list of arrays you use. If you want the old school feel, you could even assign numbers to ability scores randomly to simulate roll in order.
If you use a system that guarantees similar numbers (the card option for example), it seems like you're just using a pseudo-random system.
Not really, no, randomly determining which array is still random. I suppose you could get there, though, if you wanted to, all you need is a seed and a hashing function, and just count down the list of arrays, then back up to the top...
I don't think it's a disadvantage that I don't have the "option" of buying bread that is secretly loaded with arsenic at the store either.
If you don't know the arsenic content, it's not an option, it's a danger. If you do, hey, rat poison.
Off-the-cuff idea for a variant system that might allow a bit more range but still end up kind of balanced...?
Start with 12-12-12-12-13-13 (total 74, average = 12.33, close to the 12.24 that 4d6x1 gives). Swap points on a one-for-one basis (the total must always come to 74) to generate your stats with the following provisos and limits:
- no two stats may rise by more than 8 combined points (thus if one goes up by 5 no other can rise by more than 3)
- no single stat may fall by more than 9
- each stat must be different than each other stat
- no more than one pair of stats may total 30 or more
Workable?
Lanefan
Yeah, that's getting close to a de-facto array, just way more complicated.

Especially because of the no-two-stats-alike proviso.
1-for-1 is kinda problematic, really, too.