I think the idea for V3's dice system might've started with V2's magic system, which is a dice pool. I'd thought about developing V2's magic system as the system-wide task resolver, and my thought process went like this:
I want each 10-sided die rolled in this pool to have a 40% chance of success, so ignore all results of 5-0 (which is very much like a roll-under version of Exalted's system).
I want 1s to be the weakest sort of successes, while 4s are the strongest (just like V2's degrees of success, blackjack style).
I want doubles and triples to provide certain special effects (which is a classic V1 trick).
Since 60% of my D10's sides have no effect, if I create custom dice I can leave those faces blank. That'll same time and confusion, and it'll be easier to spot them if you're rolling a handful.
Since the other four faces on my D10 are on a scale of 1okay-2good-3better-4best -- I could just leave the numbers on them.
V3 seems to have taken things a few steps further. They have lots of different dice -- with different distributions and different effects. These are capable of providing much more information than just my 1okay-2good-3better-4best scale. They can also better control the distribution of those effects. Because they're using so many dice with so many different effects, you can end up with more than 10 symbols in your set.
Somewhere out in the internet I have another one of these monologues that explains my thought process on why cards are a neat idea in RPGs. Matching the dice effects to cards makes a lot of sense. Rather than the whole thing being one big gimmick, it actually works together really elegantly. The dice help the story by giving lots of information beyond simply numbers or 'how well' -- now it helps you tell 'why'. The cards provide a quick-reference so you can match your symbols to the 'how and why' effects. This is no different than using a skill or talent in V2. It's just on a card. The dice just have a different way of telling you how well you did, and suggestions for why it turned out that way.
It's actually kinda brilliant. It's gimmicky and expensive. It's a bit excessive, and the game might be fatally flawed in other ways. But the ideas behind the dice system are good ones, and I hope other RPGs pick up on it.
You don't need this many dice to get the benefits of using symbols and dice in this way, that's for sure. I have some ideas for custom D12s that will do most of the heavy lifting, and story-influencing D6 with a word printed on each side, but no numbers at all, just Faith, Senses, Material, Time, Fear and Chance.
But V3's method might be really fun, though. I'm willing to check it out if only to adapt to something I like better.