Pardon my naivety, but I failed to understand why is black scholes model so popular even when we know that its assumptions are violated in the real world ?

Because it's easy to understand completely and use. It can also be extended quite a lot if you want to make it more "realistic".See the in practice section in the wiki article, sums it up in a few short paragraphs: http://en.wikipedia.org/wiki/Black%E2%80%93Scholes

Black Scholes is not used to price, it's used to convert an option price to an implied volatility and back. As such, it's comparable to Yield-to-Maturity on a bond. YTM is a handy concept because bonds with similar credit quality and maturity have more similar YTM's than prices. You can graph YTM versus maturity and get a yield curve; or versus credit quality and get a credit curve. These don't tell you everything about every bond price, but they're handy summaries. The derivative of a bond with respect to YTM, its duration, is a useful number.Similarly, options on the same underlying with similar strikes and expiries have more similar IV's than prices. You can use BS to graph implied volatility versus time; or versus moneyness; to get useful summaries of the market. The partial derivatives of the BS price, the Greeks, are useful numbers.