No, it's because Pepsi isn't trying to be Coke, they're trying to be better than Coke. So having the recipe is kind of moot.

Even if they were to take the recipe and publish it for all to see, you would still need all of the other machinery that is Coca-Cola to make Coca-Cola.

And then you have issues of quality. Coca-Cola has certain standards, it's not a guarantee that everyone else will have those same standards. Like, people buy the expensive brand of milk despite all milk being the same. It's one ingredient. With quality standards given by the government. There is really no room for interpretation.