That would be cool! Are you set in your choice of probabilities? To get my math brain on board, I'd need to hear a justification for the faces chosen. Something like "this set of die faces lends itself to good game design choices because the circle/triangle can represent a more rare thing and the plus/minus can represent a slightly more normal thing, so game designers should get excited by how much easier it will be to use this die than something else"
My main thought is that choices about die probabilities (status quo, without standardized symbol dice) usually follow decisions about game mechanics/balance, so you're limiting your audience to game designers who want to make a game with the particular combination of probabilities you've provided, rather than what you're hoping, which is people first choosing your dice, then setting their intended game mechanics by the probabilities you've chosen.
I'm thinking also about how a standard 52 card deck has standardized symbols, but all the symbols in the deck are evenly distributed. Since the game designer imposes meaning on the symbols, they have full control over the probabilities.
Would you consider a standard symbol die with a different symbol on each face, possibly with only one blank face? Or some other more evenly distributed set of symbols that would be more malleable to different rules? Like some sides have combinations of symbols but it's more evenly weighted. For instance:
(I can't type a triangle)
| Side | Symbol |
|-------|----------|
| 1 | ○ |
| 2 | □ |
| 3 | ◇ |
| 4 | ○□ |
| 5 | ○◇ |
| 6 | □◇ |
In this example every player has a complete understanding of the set of symbols at a glance, and the game designer can assign their own meanings to the symbols. I would honestly be the most excited about standardizing a die with a different shape on every side, and really leaving full control to the game designers.
I get it if you totally disagree with what I'm saying, because I agree it would be cool if they standardized the dice you yourself came up with. Just airing a thought. Thoughts?