1. Most tasks don't really boil down to a single Stat. Think, for instance, of climbing a sheer wall. Is that DEX because it requires agility, STR because climbing requires you to support your own body weight, CON because it requires you to be fit, or INT or WIS because it requires you to think about where handholds are and apply climbing know-how? Roll-under-a-Stat, then, seems a little reductive.
2. It puts emphasis on thinking about Stats, which isn't as bad as obsessing over skills, but still can be restrictive ("I won't bother attempting difficult task Y because my character's Stat X is crap").
3. I think I would find myself using it as a lazy shorthand to stop me thinking carefully about PC actions in the game: "Oh, you want to negotiate with the guards? Roll CHA."
I prefer nowadays a method which I think is more intuitive and more humanist (!). That method is as follows:
- Player says their PC might do something
- DM considers the situation in general (including the Stats of the PC) and assigns a target number for success between 1 and 6
- DM tells the PC what this number is
- PC decides whether to go ahead or not and has a small amount of negotiation
Let's use an example: Bob the Builder is a PC and he wants to get some item of treasure which lies at the other side of a moat that is filled with killer crocodiles. There are vines hanging down from trees which overhang the moat. Bob's owner decides he's going to try to swing, Tarzan-like, across the moat on one of these vines. The DM thinks for a bit: intrinsically, the task is relatively difficult but not immensely so - we've all played on rope swings as kids. Bob the Builder has a STR of 15, a DEX of 9, and a CON of 12, so the DM reasons he's in pretty good shape. He says, "You can do that if you get a 3 or more on a d6. Otherwise you fall into the moat. Want to go ahead?" The player can then say yes or no. He can also, if he thinks the number is egregious or the DM is overlooking something, negotiate. Let's imagine the DM forgets that Bob the Builder has a STR of 15 and puts the target number at 4. The player howls in outrage: "But Bob has a STR of 15!" The DM relents and makes it 3, and so forth.
Now, this is necessarily somewhat arbitrary, but there's an antidote to that.
So, then, what's the point in Stats, exactly? In the noisms school of D&D, there are three reasons for their existence:
A. Stats provide flavour and a role playing guide. They stop PCs just being another PC. Why does this guy have STR 6? Is he just a scrawny weakling or does he have some debilitating disease? Why does he have DEX 4? Is he blind? etc.
B. Stats help you decide which class to be if you're rolling 3d6 in order and seeing what happens.
C. Stats are something to take into consideration when checking for success. To refer back to the example above, Bob's STR, DEX, CON etc. are relevant considerations. They're just not the only ones.