One thing that everyone forgot to mention is that the fact that the stats are not very granular is nearly immaterial to the gaming. For example, let's take one of the most common set of CHA:
STR 13
DEX 18
CON 13
Now these are all great numbers and extremely common. But so what. It just doesn't matter if everyone has the exact same numbers. I mean, who cares if one person can list 5 pounds more or less than another. It's just not that relevant.
Take those three stats above. They work equally well for a nice combat-mage, a great archer, or an amazing thief. They would also be fine for a master fencer. So, just because those four different characters all have the same STR, DEX, and CON, are they all the same? Of course not, they'd be totally different.
And really, if you think about it, that simulates real life pretty damn well. Minor physical differences between people are almost totally irrelevant. Think about it. I would guess that for most of you, strength-wise, you are able to lift within 15 pounds or so the same amount as the vast majority of your same-gender friend group. Of course, there's always a few who can lift more or less, but, I would bet that nearly everyone you hang out with of the same gender can lift nearly the same amount. Does this make you all the same person, or "character" as we say in gaming? Of course not.
So, my suggestion would just to be to ignore the "granularity".