I'm all for no need for specifing what kind of resource you dig. If there are few in the spot you found (these pebbles you talk about), it goes randomly.
I don't know if i got you right. But what about claiming for a pebble, just like we do with mobs? What you leave to others, will be free to take/mine (without claim option anymore) and as you say disappear with time. ( sink to ground just like all these items dropped in FPSes?

(WolfET especiall))
There would be that so wanted luck factor, because you could be sometimes very lucky to find eg giant gold nugget inside rock ;P Just look how people kill these rogues in search for some special weapon

The luck factor would fit there really good.
Maybe the luck could be increased slightly, when you have
prospecting skills and take time to actually prospect? I believe we really need prospecting, about it
later.
Also, i would like to inform that platinum is often found in gold mines.
What about sand for producing glass? I know there are also mines for it, but what if in PS it would be brough with a river from somewhre outside Yliakum? We would have logical explanation why it can be still founf in places where already collected. River brought it.
I expect the rivers to be lit bigger in different seasons (i think even setting on PS site say about it), so after these seasons, the rivers going back to normal amount of flowing water, but with new spots of sand on its banks

EDIT:
Ah yes, the
later ;P It's
where prospecting skill would be of main use, which is looking for these spots on bigger area, where the resource may be found.