I think the most telling part for me is that die rolled characters are almost universally higher point buy value than standard. Yes, there are exceptions, but, generally, anything that's really low gets tossed. Several people in this thread said exactly that. So, it's not so much about getting random stats, although that's part of it, but, IMO, it's mostly about getting better starting stats. I mean, heck, even the OP's die rolled character is significantly higher value than standard with four base scores sixteen or higher.
I hear all about this or that die roll method, but, again, funnily enough, all of them skew to higher than standard value. Other than the 3d6 in order hardcore version which gets some notoriety, I've yet to see someone start promoting a random chargen system that would baseline at standard point buy or even baseline lower than standard.
I'm not really convinced that it's all about playing to weaknesses when the OP's character is basically the equivalent of a level higher because of its stats.
I do agree with your argument, and I can't believe how many of the people here have been talking about the level of forgiveness they themselves as DMs or their group DM has allowed when rolling, but the nearest thing to a reroll that exists in my group is one swap that is you can change one stat for another no rolls, no additional dice. The first system I ever played was Rifts and they have a really weird dice rolling system that allows for some absolutely insanely unbalanced parties, you roll 3D6, if your roll is under 18 that's all you get, if you roll 18, you roll another die 6, if it comes up 6, roll another, this continues until your starting stat maxes at 30. And in Rifts your character gains no attribute points ever, no items increase them, leveling up doesn't increase them, so whatever your stats are, are what your stats are, also there are no racial modifiers, and we played that rule to the T. I played a lot of terrible stat characters in that game, I played in Palladium (which has the same rolling and leveling system as Rifts) a Dwarf Monk in a party of Dwarf's that had the following stats (stat names changed to D&D titles)
Str: 12 Int: 6 Speed: 11 (you roll speed in that system)
Dex: 8 Wis: 8
Con: 9 Cha: 3
In the Palladium system 12 is the lowest number without a negative modifier, I had no bonuses, I played him anyways, and I struggled every session to survive every encounter, and being a Monk, I gave 90% of my wealth to others, I never once bought a magic item, I found a few useful ones, I completed the campaign with him (we closed the campaign at 12th level).
That isn't the only
horrible character I have played, I was once forced to play an Elf, because the other character wanted to be a race that only the elves didn't want to kill on sight, I hated him and basically tried to kill off my character by being reckless all the time, survived being KO'd a sickening number of times. In D&D I have played some horrible characters, some amazing characters (like my current) and some interesting characters (where I didn't have two stats that were compatible) but I've enjoyed playing every one except for the two I've played point buy, because I played my point-buy cookie cutter and wound up with an *average* character, I would honestly rather get stuck with that monk dwarf that an average character, because I'm strange as all get out.
*Edit* I just had the thought that in Rifts you may get to roll an additional dice (the first time) if it is 16-18.