Market efficiency is not a moral concern; it's more like a physics observation.
In fact trying to understand economics with morality or some other form of normative claim is a huge and quite pervasive mistake that destroys people's ability to understand it before they even start trying. It's a machine. What we do with it may be moral or immoral, but the market itself is all but a natural force.
At the very least, if not me, Warren Buffett has shown that the market does in fact exhibit large-scale persistent opportunities. You just have to be patient. I don't think "arbitrage" is actually the relevant term here. It has a very specific meaning that isn't simply a stock being mispriced. Really though, the market offers deals all the time.
FWIW, I don't have Buffett's track record, but I currently have 20 stocks in my portfolio most of which I've held for several years. Of those, 19 have made money and 1 has lost a small amount, and on the whole I've beaten the market nicely. I could just be written off as lucky, or as about to lose lots of money, but how do you explain Buffett? He has a track record of consistently beating the market by wide margins for 50 years. Seems like that wouldn't be possible under EMH.
[1] http://www.investopedia.com/terms/e/efficientmarkethypothesi...
As for your positive returns, the easiest explanation is that you're in a green square on this graph (suitably updated): http://www.nytimes.com/interactive/2011/01/02/business/20110... (Read what the graph is carefully, most people misinterpret it at first glance.)
...on average. Which is what makes "beating" the market, over enough time, impossible.
But we know there are pricing discrepancies and information asymmetries in finite periods of time because we see them every day.
The EMH is false for values of "efficient" that are interesting, and the values of "efficient" for which it might be true are boring and useless in the grander scheme of things.
A lot of needless bad blood enters discussions because everybody interprets the word "efficient" as they please.
But I'd be selling it, and you can find out how by buying my book for the low, limited time price of three payments of $99.99. If you act now, we'll also throw in this great place-mat shaped like a $3 bill, and a ring-tone for your phone that sounds like money. Just pay separate shipping and handling. <insert three thousand word disclaimer here>
Knowing that the market is inefficient is not equivalent to knowing which stocks to buy or sell, or when to do so. It doesn't give you a magic formula, but it does give you some idea of what to look for.
FWIW, I have done pretty well picking stocks for myself, but I'm far from what I would consider "extremely wealthy". That being said, if I had a magic formula for instant huge wealth you can be damn sure I wouldn't be sharing it.