Let me say first that if anything I've written has implied that your playing the game wrong, I apologize, as that is absolutely not my intention. Again, I use both styles depending on the group and our goals, so I get that both are fun! And I get that you like and prefer PointBuy, I'm just truly interested in why. It sounds like perhaps it's about having control of all the details of your character, is that a fair conclusion?
On the other hand, I would like to understand some of your conclusions about Random style.
For example, I don't see random rolling as creating a random PC. Random rolling can create Tormond the warrior fleeing from his pirate king father..etc...etc, it's just that the seed for that idea comes from a different place. In the case of Random generation, in my eyes the difference is that Tormond the warrior may want to confront his father and make him pay for his sins, but because he was born without his father's inherent strength, he will have to adventure for many years to gain the strength necessary to defeat him. Now, I don't have control of that narrative before I roll, it's one I come up with after the roll, whereas you may build your character to that concept.
As for Chuck the Waterboy, if I actually rolled a character with nothing but 3's, I would look at it as a unique challenge of my skills as a player, but it is extremely likely that I will have at least one stat 10 or higher after racial bonus, meaning I'm more likely playing Chuck the star offensive linemen instead of Chuck the star quarterback. Chuck the offensive linemen is still the hero of his own story, I as a player just didn't have as much control over his starting conditions and had to come up with his story as a reaction to the die rolls.