Dice are, to me, an answer to a question. If I already know the answer to the question, I'm not sure what dice have to offer. If I don't know the answer, then yes, dice are great.
Where it gets weird is when I have one answer to the question and another player has a different answer. Dice are absolutely a way to determine which answer is right, but I am starting to wonder if it's a good way to do so. it feels like throwing out some amount of mojo (and consciously avoiding a shared understanding) in favor of oddly shaped oracles.
In the absence of dice, such a disagreement might be born out of hidden information - you as the player may think your guy is a better swordsman than the black knight, but I as the GM may have a different understanding. That's fine, that's high-trust GMing, but it works.
On the flipside, dice make a lot of sense in the absence of hidden information. if the players know everything the GM does, then there should be clear consensus regarding which questions don't have clear answers.
But when there's hidden information and dice? That seems like an invitation to trip over your own feet. It's also the most common arrangement in gaming, so it can obviously work, and that fact casts an interesting light on the role of trust. The success of hidden information corresponds directly to trust, which seems obvious, but gets interesting when you realize that dice are often considered arbiters, more 'fair" than the GM.
And that seems self contradictory - trusting the GM enough to allow hidden information but using dice as some sort of totem of GM distrust seems... kind fo screwed up.
None of which is to say dice are bad. But it's making me think a lot more about those times reflex demands that I turn to them.