I can't be the only one who thinks it's strange that dabbling miners destroy stone. So my idea is that instead of making the mining skill determine the chance of finding anything useful in the material make it decide the weight of the stone found (sort of like checking for purity). So that a highly skilled miner will only mine out the gold while a dabbling miner will mine out all the useless material around it. Once it is made into something it's weight will go back to the normal value. It would tie in nicely with the current minecarts thing as a dabbling miner would leave very heavy rocks which are almost impassible to move.
I always took it to be that a low-skilled miner destroyed the rock in as much as being used for other tasks -- so there simply wasn't enough uncompromised stone to carve out a door, for example, because the novice miner just hacked away at the rock wildly rather than actually getting a nice, large area of stone to re-use. Now that does discount tiny objects, crafts and toys and such, but then we get into sizes of stone for various items and it gets rather complicated (and what happens to the scraps?).
Likewise, failing to mine out ore is simply not knowing enough to get the ore properly and it gets mixed in with chips and garbage that presumably are too small to be concerned with, or are just a part of the area being "rough", and the engravers clear it when they smooth it.