It should be included in the explanation of bitcoin, but it shouldn't be the main point, more on the level of the block chain in importance, and the important thing about mining is that it keeps the network safe, and for that work you get a reward.
Any serious person who will look at BitCoins one the first things they'll notice once they learn about how it all actually works is what I now understand. And that is that right now there's around 3k nodes and 5,5mio coins out there. And these 5.5mio coins are being held a by a small minority, probably far less then 3k. And there's no way the trading price of $0.9/BTC is realistic with such a low volume and so many people sitting on their stash.
And before you read my reply any further let me make it perfectly clear that I don't care how many who has. I understand what this invention is about. I'm an an-cap supporter and an austrian economist first and nothing would make me happier if the whole world would use a currency that couldn't get hijacked by governments and inflated at will. But that's not your typical user and never will be.
If you want this invention to really take off you can not have a small minority who will sit on all the coins and suppress the supply in order to bid up the price because people just wont buy. What you need is more people who own some, not because they bought them, not because they charged them but because they also mined them. It's irrelevant why these people hold some as long as they do and if they trust BitCoins they'll start trading them with others and the volume in trades will build up and BitCoins will gain mainstream credibility.
I mean do you really think gold became world wide currency because select few people had most of it when it was first discovered? Of course not! People all around the world found some, some found more, some found less, everyone though shared the same opinion about it and eventually they started to trade it as money.
I have a feeling that there's a lot of brilliant minds on this forum when it comes to software and computing who utterly fail when it comes to history and economics and especially human nature. You got to understand these things if you want to see this invention really take off.
p.s.: I call it an invention because I can't really call it a commodity because you can't make anything out of a BitCoin but it's also not a currency, not just yet.