I don't agree that they serve the same purpose; shorting is not the same as buying a put and the two only behave similarly in a very narrow and limited sense that isn't particularly practical. Yes in some circumstances money is gained if the price of a stock decreases with both a short and a put, but the risk profile, timing and cost are quite distinct.
Furthermore it's absolutely possible and in many circumstances likely that the price of a put decreases even if the underlying stock's price decreases, for example if the volatility also decreases.
I don't think many informed individuals treat shorting stock the same way they treat buying puts nor do they attempt to accomplish the same purpose.
I didn't say they were the same, but they serve the same purpose. Buying a put is a long volatility and short underlying position. You can mitigate the effect of volatility with spreads. But the directionality of the position is what you're buying with a put, you're buying delta within a certain time frame. And as I said, the risk profile of put or well constructed spread is better than plain shorting which has unlimited downside.
Furthermore it's absolutely possible and in many circumstances likely that the price of a put decreases even if the underlying stock's price decreases, for example if the volatility also decreases.
I don't think many informed individuals treat shorting stock the same way they treat buying puts nor do they attempt to accomplish the same purpose.