ELI5: Why do derivatives (puts and calls) exist?

I see the argument that “it’s a price-searching mechanism” for the stock, but that price-searching already occurs at the initial price without derivatives pushing or pulling the price further than that initial valuation.

For example, in a non-stock setting, a can of Coca Cola may cost $1; that is what the market bears. It doesn’t need puts and calls to further “price-search.”

Derivatives came from Midwest farmers hedging their bets against a bad harvest. The secondary derivatives market today bears no relation to that.

Bottomline, I think puts and calls are legalized gambling that serve no intrinsic economic purpose.