I define an elegant RPG as one that is simple and gets the job done. 3E D&D isn't it. The one that suits my tastes, and lets me use all the inelegant OD&D, 1E, 2E, and 3E material I want with relative ease is C&C (Castles and Crusades). It uses the d20 mechanics of positive AC and positive saves, then has a wonderful abstract system that allows every character to attempt to pull off a feat like maneuver or effect, and skills for each class are based on common sense, not defined lists, unless I want there to be a list, so there is.
Sure the classes are iconic, but with being able to use virtually any feat from 3E (that doesn't increase a skill check), a "common sense" list of skills, I find the characters to be a lot "KEWLER" than the restricted characters tied down with "feat chains" and skill lists. Plus we get to concentrate on having fun and creating a cool story together, not referencing rule books and not spending a half an hour or more levelling up characters trying to decide on which feat I want to take next.
I find roll your HD, add your base to hit, and up your level number, lets game, to be a lot better.
So C&C is my personal definition of "elegance". Its the D&D game I waited almost 20 years to be created. I have to thank 3E for that, because without 3E C&C would never have been created. C&C is a d20 OGL game for a reason.
Plus I have to admit 3E is a good game for people to start out with. Everything, and I do mean everything, is spelled out for you somewhere in the rule books. One of them. Which one is your needle in the hay stack to find, but it is there. The most relevant likely being in the PH or DMG.
That is why my kids prefer DMing 3E. They have rules telling them how to DM. When they feel "comfortable" with knowing the rules they will switch to C&C. IE they need to be confident in making rulings that aren't backed up in black and white print. Even though every rules question that has come up in the C&C game has been covered.
For the record I still play 3E, I'll just never DM it again.