Can you show me the webpage that states that Long call + short put is a synthetic call? As far as I know, it's NOT a synthetic covered call. Edit: As many have said, it's synthetically longing a stock. When the stock goes up, you do NOT automatically own it either. You have the option of owning it. There is a difference. It is only a reasonable strategy to buy a stock that you think will go up in very limited scenarios. In general, it's not because you are buying a stock at a higher price than the market price when you are assigned the stock through your short put. It's not really an efficient way to own a stock as far as price is concerned.
It does not lower the cost of buying a stock. You will be buying the stock at a higher price than what the stock would be selling in the market because you will be forced to buy the stock when the put buyer exercises its put at a strike price that's higher than the stock's market price. If the stock hasn't tanked to lower than the strike price on the put, the put buyer wouldn't have exercised the long put. So you are actually buying a stock that's going down.