The work is invented on purpose... Key word is PURPOSE rather then "for the lulz".
Smoke and mirrors also have their purpose. Actually I would value a financial instrument backed by lulz (comedy gold) higher than an instrument that essentially represents humiliation, jobloss and wasted electricty (actually to more mean spirited people that would represent lulz). The only rational actor I can think of who would actually invest in it long term, would be the power companies in markets with many miners, or hardware manufacturers, if they could use it as a instrument of electricity waste and hardware futures.
Note that I'm talking about bitcoin as an investment here - I'm not knocking it as a transfer system for quick payments. Only intraday stability matters for that.
The "invented" work is also known as cryptography and its purpose is to stop anyone from printing infinite coins as well as to ensure the system is unadulterated by fakes.
The why is to prevent fraud
Fraud is rampant though.
More importantly, once the security is high enough that the computational difficulty to break it would need much of the output of the sun, throwing more computation at it is useless. It might as well be backed by proof of jumping up and down in your living room.
It just becomes a game of chicken where those who can keep mining going for the longest can try to keep the value up, but then the last guys get stuck holding fantastically secure tokens that nobody else cares about, specialty hardware, and an electric grid connection that's ready for Vehicle-to-grid or starting their own mini power plant. Hopefully they didn't spend too much fiat in propping up the value of BTC to make their mining investment profitable.
Its bad enough when the government is printing infiniate money, give that power to every citizen and you got a worthless "currency".
Isn't that what Bitcoin initially tried to do? If every computer owner in the world could easily process transactions, without having to invest in specialty hardware, I'd imagine that the system would be more robust than one that encourages consolidation of "mining" power.
Can you come up with a way to ensure every living person only has 1 wallet? (answer: no... unless you are the government and institute some strict biometrics)
Even if governments get involved in some capacity, that doesn't mean that we give the control to ONE government or ONE corporation. The free market would still exist, and devalue the real value of a currency if they think there is a lack of transparency, or fraud.
Even if you distribute the issuing rights to entities that are unlikely to be influenced, there is no way to guarantee that these rights won't in time consolidate in the States' hands.
You could make it illegal to control more than one issuing authority. Besides, the problem of over-consolidation also exists with the current Bitcoin protocol.