> You, too, don't understand the fundamentals of Bitcoin.
> The nonce must be brute-forced to prove that the computing power was expended. It is precisely this expenditure of computing power that makes it expensive to cheat.
No, I understand why it's done. But it has no practical use outside of Bitcoin.
In the real world, we pay people money for useful work (a gross oversimplification, but let's keep going).
Imagine a world where it's impossible to print money, and the only way to create money is by drawing dollar bills by hand, which is a very difficult task. Surely, people are being paid for their work here? Well, yes, but if the work is going only into the creation of the tokens, then it's useless. Why would you want an economy that revolves around the value of having wasted computing power on a nonce value? Maybe if we assigned tokens to those who expend computing power on medical research or the like, that's more useful. But Bitcoin is a waste of resources to generate.
http://primecoin.io/ is an example where the work being done is useful - it is used to discover more prime numbers.
However, regardless of the "usefulness" of the actual work, it ties the value of bitcoin to a very tangible resource: the amount of mining power available in the network. This is actually more similar to the gold standard than fiat currency, where proven reserves are needed to print more currency.
Is there any cryptocurrency that already does useful work in its mining? That seems like a great idea. You could incentivise people to do things like protein folding as long as you could also make sure the work isn't fakeable somehow (which I suspect is the big problem here).
There are three that try to find primes - Primecoin, Riecoin, and Nexus. This isn't "useful" but it's a bit more intellectually interesting than finding partial collisions in sha-2. (I wrote the miner that's now used for Riecoin.)
There have been attempts to do others but none that really work, because in part of the problem you cite. It's also very hard to have a tune-able difficulty for the mining process.
> The nonce must be brute-forced to prove that the computing power was expended. It is precisely this expenditure of computing power that makes it expensive to cheat.
No, I understand why it's done. But it has no practical use outside of Bitcoin.