I have a difficult time becoming emerged in events in a D&D world when the dice used in the event are exactly the same as another event (namely combat). If social situations were resolved using a d12, and the variables were different than say a d20 combat, than I suspect the feel of the event would be different.
Take something like 3e/4e combat. Damage uses a different type of die than the attack roll. Even different types of weapons use different dice. When you roll that d12 for an axe swing, it feels different than if you were rolling a d8 for a long sword. All damage feels different than the act of rolling to hit.
Spells feel different since the rolling part (in 3e and previous) is done by the target, not the caster. When you say "roll a saving throw" it feels different than if you roll the d20 yourself.
If you're exploring a room and roll a d6 to look for a secret door, it feels different than rolling a d20 to look for it. You don't associate the action with an "encounter" even though the door could be trapped or another event may occur.
Sure it's easier to roll the same dice for everything, but the cost in 3e and 4e is that every event feels like combat, even the mundane skill checks. I felt like I was attacking a wall to climb it or attacking tracks in the snow to follow them. D&D has a long history of crazy looking dice, I'd like to use them more often.
A unified mechanic can use the same dice for the same types of situations, it doesn't need to roll the same die type for all situations. Social situations, d12; Exploration d10; thief skills, d100, mundane skills d4, searching d6, etc. If every time you rolled a specific type of die for a specific situation, that feels pretty unified to me and feels like you're doing something different than attacking something.