Why is this impossible? And why is non-combat so much more campaign dependent than combat?
One player in my 4e campaign has the bulk of his feats as non-combat ones (multiple skill trainings, linguist, ritual caster, etc) and also has an epic destiny whose 21st level benefit is non-combat (Sage of Ages, which grants +6 to all knowledge skills rather than the standard stat boost). As a result his PC is less effective in combat than some of the other PCs (though not too shabby) but clearly the single strongest PC in non-combat situations, especially those involving magic and lore. (But the same PC has a head slot item that boosts combat - bonuses to avoid dazing and stunning - whereas another PC whose feats are mostly, perhaps all, combat related has a head slot item that grants +2 to social skills.)
I don't think that balancing combat and non-combat need be all that hard, provided the non-combat abilities are clearly meaningful in play.