Here's a crazy idea: what if players were free to pick and define the ability scores that would go to defining their characters? Not the score but the abilities themselves.
Let each player create at least two up to maybe as a dozen ability scores. Have each one get a one line description and up to 3 game things that ability score can modify, with no more then 2 ability score allowed to overlap one game thing. This isn't a communal thing each player picks their own list of abilities. Have the players generate scores afterward.
You could end up with:
Elfus the Fighter/Magic-user
Magic 14, +1 to hit with magic weapons, foes save vs spells at -1, +1 save vs magic
Aribel the Wanderer
Courage 16, +2 to hit in melee, +2 save vs fear
Perception 14, +1 find secret doors/searhc for traps, +1 intiative
Bushcraft 5, -2 tracking, -2 foraging
Blather 13, +1 reaction roll, +1 minion morale, +1 distract
Fozworth The Fabulous
Presence 13, +1 to reaction rolls
Comeliness 14, +1 to reaction rolls
Voice 8, -1 to magic attacks
Grace 14, +1 to balance, climb, and dodge
Will Power 6, -1 to save vs spells, psionics, and temptation
Seduction 14, +1 to tempt others and distraction
Sure occasionally contests between characters and tasks may be difficult to arbitrate now and again but: DMing and Palyer roleplaying can meet somewhere in the middle.
*Elfus and Fozoworth are having a foot race it's a contest of Might vs Grace.
*Elfus and Aribel are having a debate in public in front of witnesses about locla politics, after the players do a bit of stumping for the crowd it could be resolved as contest beten the Might of Elfus (if the player thought to have his stumping intimidate the crowd with physical preference) vs the blather of Aribel who can string on endless streams of locution.
* A stout dungeon door needs to be opened. Elfus might see this as a test of Might, Aribel as a challeneg towards Stature and Fozworth may have to resort to picking the lock with Legerdemain.
I wouldn't mix this with a detailed skill system as skills players want can be worked in as an ability score or a modifier.
So what do you think?