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I find it strange in all trek series that cultures who use matter transporters (some of which have for centuries) still need or choose to dig for their metal like savages- why can't or don't they just beam the needed minerals right out of the rock?
It would be depressing if no one thought of this before me- are there environmental concerns? Would it put too many people out of work?
Generally speaking, you have a very little bit of ore for the mineral you want mixed in with a lot of unwanted rock. For example, solid nuggets of relatively inert metals (like gold) larger than a few grams are extremely rare - and it's harder for more reactive types, and the rock generally must be ground up, filtered, smelted, or otherwise processed.
Of course, Star Trek transporters are able to scan and replicate at the quantum level, but we only ever seem to see them used to move large, contiguous objects (people, cargo containers). We certainly don't see lots of extremely small objects being selectively transported. This probably means that extracting only the wanted mineral from surrounding rock is technically prohibitive.
Also - it is unclear how broad access is to transporter technology. Most Federation ships we do see in Star Trek are Starfleet, and so we would expect transporters. But quite a few non-Starfleet ships do not appear to have their own transport system and require docking/landing (such as the miner's ship in Final Mission).
In addition to the points HorusKol made, there's a few things that have been shown to consistently block transporters in Star Trek. One of the major ones is large deposits of some ores. Another is technobabble (which is often explained by natural things like ore deposits or atmospheric conditions). The last is large amounts of earth or stone.
The final point is inconsistant - Wrath of Khan featured multiple transports to a system of caves that were deep below the surface, for instance. That said, the space station they were on had regularly been doing so as part of a long-term scientific study, which indicates that they may have done something to enable it - extremely specific coordinates or pattern enhancers or something similar.
I would therefore say that the conditions in which the metals and ores that cannot be easily replicated exist would most likely be conditions which preclude transporter usage.
The short answer is "they don't do it, because they can't." The technology for discretely picking out just the materials you want simply doesn't exist... yet...
In TNG, Episode 6x09, "The Quality of Life" the Enterprise is evaluating a new mining technology, the Particle Fountain. While it is not thoroughly explained (as it wasn't the true focus of the episode), the name and appearance of the device indicate that it has the capability to extract individual particles of matter and bring them up to the station. It's described by Picard as "radical", which is strong evidence that nothing even remotely close has been done before.
