The mining in the Manual of the Planes is overseen by the Dao, mostly. Who use slaves to keep the cavern they're in from collapsing and tunnels maintained. It's mentioned as part of inter-planar trade going on.
In that case, even though the infinite number of Dao mine an infinite amount of gems, gold, copper and so forth every year, it's highly unlikely that the mining represents any regular trade with your average prime material world like Krynn, Toril, or Oerth. The amount of Earth-stuff (or fire stuff, or whatever) imported directly to a prime plane is probably in balance with what is removed from the plane to pay for it. And even so, the total trade with any one of the infinite number of prime material worlds and alternate realities is probably as negligible as the total amount of goods of infernal origin that enter a plane as a result of persons selling their souls to interloping devils. There is no reason to suppose that mining on the elemental plane of earth necessarily has a large impact on any published setting, despite the infinite quantities of ores thereby mined. Presumably only an infinitesimal fraction of the infinite number of elementals is even aware of or could ever contact any particular reality. Ditto the infinite number of devils, etc.
Presumable the greatest percentage of this infinite production is traded with the infinite number of inhabitants in the outer planes, other elemental planes, and the like. Likewise, if the Dao are using slaves, there is no particular reason to suppose all or most are inhabitants of the prime material planes. There are after all an infinite number of mortals native to the non-prime planes per planescape, inhabiting an infinite number of border towns. And presumably places known to every reality like Sigil, the City of Brass, or Dis each have an infinitely large population in and of themselves. This makes trade with even Toril completely unnecessary, and with anywhere less cosmopolitan particularly unlikely.
Hopefully, you recognize my slightly mocking tones regarding the infinite outer planes. I don't know what percentage of DMs insist on the infinite alternate realities of Gygaxian D&D, but if you don't insist on them, then the very notion of a single finite 'prime' with infinite externalities becomes weird in the extreme if not down right nonsensical. And if you do insist on them, well, your cosmology is now impossibly complex.
The issue of elementals using local material gets iffy when you start talking about interplanar gates that allow directly crossing over; I don't think the idea of material works out, as it doesn't explain why the adventurers do not suffer the same if they cross into another plane.
Read up on Astral Projection in D&D for example.