In my area, stone dust comes in a variety of sizes but it is hard to find a super fine stone dust . Over a short amount of time the fines filter down and the larger particles rise to the top.
This makes it a good intermediate base especially if you are topping off the court with oystershell flour, but not a good finished playing surface.
You may be able to find a finely granualize stone dust in your area in which case it would make a good finished surface. In my area though , the stone yards don't carry a fine stone dust like they do in other regions of the country. ( that's one reason why you see decomposed granite used )

I've used dg to build courts with and due to the relatively uniform size of the particles it makes a more suitable intermediate as well as a satisfactory finished playing surface.

A stabilizer makes the surface more durable and there is still enough of a grainy texture.

If you can locate oyster shell flour it makes for a nice finished playing surface, especially it you have a custom mix that uses a little clay in the mixture.

Our regular building specifications use 3/4 compacted drain rock, a 3 inch sub base of permeable stone dust fines ( which is not like east coast stone dust fines ) and then cap it off with a leveling layer of clay + oyster shell mix

I buy a local finished product here ( Northern California ) from Jerico Co located in Petaluma Ca.

Attached are a couple photos showing some bocce courts with different finished and unfinished materials.
The modern looking court has its base and subbase installed . It doesn't have the oyster flour + clay mix added yet.

The bocce below is finished with oyster flour and is surrounded by stablized decomposed granite {{gwi:27369}}From Sonoma - Freudbrgr
{{gwi:27370}}From Sonoma Valley Project