> If so, why does it make sense that people can "generate" cash by proving some amount of work done?

Think of it this way: If you pay with physical cash, there are people somewhere who do the work of digging ore out of the ground, smelting it, shaping it into coins, cutting and printing paper and so on. All these people do that, because they get paid in the same currency that they themselves have minted.

It turns out that nobody has yet found a way to create a digital decentralized currency that that works without incorporating a similar concept of incentivizing the creation of currency.