There's gold in them there digital environments!
When you're roleplaying in an online computer game, you have to accept a lot of the things you cannot change. It may seem illogical that your character has to go digging in the dirt by him or her self when people in the real world hire others to do that for them, but nonetheless that's how things work. It's hard to create any scheme by which you hire other people to do the mining for you, because the value of the minerals acquired only increases with the skill and level of the character involved. Any person you might want to hire to collect Saronite for you could just as easily go and sell it on the auction house themselves without having to pay you even a middleman's fees, much less settle for a laborer's measly wages. The controlling limitations people can put on one another in real life (such as restricting access to buyers and markets) just aren't there in the game. If someone is rich enough to buy all the ore he wants, it doesn't mean he's exploiting workers to do the mining for him, it just means he gets his wealth by some other means.
So if the game can't change, our idea of the world we play in has to change instead. Here's how I make sense of it: Ores in Azeroth are like bubbles that develop from deep inside the world and slowly make their way up to the surface, where they pop out of the ground at various soft spots, kind of like very minor volcanos, only without all the nasty lava. The earth just upchucks nice little nodes of precious metal and seals itself up again.
Simple metals like copper are relatively easy for anyone to just come along and hack away at, as long as they have some basic training with a pickaxe and willingness to get their hands dirty. But as metals get increasingly complex and valuable, they also get more difficult to extract. You can hack away at Saronite for hours and still not get a single speck of it unless you hold the pick in just the right way, and strike at just the right point. Once you have the skill, it comes easily, like a well-practiced card trick.
This skill required, combined with the danger surrounding most of these metallic soft spots, means that only great adventurers are capable of actually acquiring valuable ores. These adventurers are, of course, well connected, so you wouldn't find them handing their profits over to someone else unless they did so through some relationship of cooperation and reciprocity.
Earth is what we're made of
And that is precisely the reason why dwarves are so enamored of digging for ores and metals. Something that takes a lot of skill and power to do, and then returns a great reward is more likely to be seen as a very desirable profession. Some societies might even base their cultural identity on this, especially if they have reason to believe they were once made of metal and earth themselves.
But even if you're not a dwarf, there's good reason to take pride in being a miner. After all, minerals are highly sought after by three other professions -- more than any other gathering skill. Not only can you make a lot of money off of it, but you can also provide an excellent service to people who need what you've got (including yourself in that if you happen to also have one of those three professions).
Earth is for other people
Nonetheless, mining isn't going to be something everyone does with dollar signs in their eyes, giggling all the way to the bank. There are lots of reasons your character might avoid mining completely, or undertake it only with the utmost reluctance.
The first and most obvious one is that mining is rather dirty. A number of adventurers simply prefer not to get their hands covered in dust and grit. To them, something cleaner, like tailoring, is much more attractive -- or perhaps enchanting, if they prefer magical dust to the more ordinary sort.
Personally I'd love to see some miners shrink away from ores they find, offer them to other miners first -- almost beg other people to take them -- and finally only take up the pick with utmost reluctance once it's clear that they're the only ones with the skill to get the goods. I can imagine a blood elf, human, or any character really, complaining while they hack away at the ore, wishing they didn't need this stuff for their sophisticated engineering experiments and wondering if it would one day be possible to build a flying machine out of herbs instead.