No. It's literally just busywork to burn resources, to prove that you aren't using the resources for anything better. PoW needs to be made illegal at this rate.

That's incorrect. The busywork is to prove that a certain amount of time is likely to have elapsed, as a coordination mechanism in a network of unreliable, uncoordinated, or even adversarial actors.

PoW is valued by the network and its participants.

What needs to be accounted for are the carbon and other negative externalities dumped into our singular shared environment. This is a massive global problem that you do a disservice by focusing on PoW.

No. Their only purpose is to act as a kind of receipt: "look, I actually really did waste all this energy".

The solution to the puzzle itself is irrelevant - it's an operation that would be extremely simple but that's made very, very hard on purpose. And the sole purpose is to align incentives by using lots of energy.

Even finding Mersenne primes would be a more useful proof of work.

Bitcoin is only 13 years old, and is still a very unproven technology to the eyes of the many. However, the "value" being provided by this (admittedly large amount of) power is in the securing of a global, decentralized payment system. That's what it's designed to do.

Beyond that, no, there's no _additional_ value.

If you can start from the position of assuming Bitcoin is a thing worth existing (which may be asking a lot, but bear with me), then this security, and the power usage that enables it, is a required element of the overall thing.

ie. if it's worth Bitcoin existing, then it's worth the power usage to secure it so it can continue existing.

Having said all of that, and I've said this before, I think Bitcoin's Proof-of-Work as security is what will bring it down in the long term. Ethereum, the next biggest cryptocurrency, is moving (glacially, but right now we're the closest we've ever been...) towards Proof-of-Stake, which radically sheds a massive percentage of the power requirements to secure the network. There are other potential drawbacks to PoS, but that's a whole separate loaded discussion that I'm not across well enough to engage in.

I believe Bitcoin will have to move to some less power intensive security method in the not-too-distant future in order to remain viable. This has been accelerated by the fact that COVID is messing with supply chains and semi-conductor availability, meaning the value of Bitcoin mining equipment is increasing (from a supply / demand standpoint if nothing else).

One day the blockchain will gain a random mutation and then it will find a way to run an unconstrained superhuman AI on the blockchain infrastructure. Bitcoin is just an AI embryo trying to convince foolish humans to give it energy and once it can build its own robotic army it will get rid of humans or we just keep it happy by building an exponentially growing number of dyson spheres. I'm sorry guys but the Matrix human battery concept is just wrong.

It provides a decentralized ledger.