While there are definitely valid concerns with just how much energy we spend maintaining the bitcoin network and the blockchain, it's hard to call it wasted and it's definitely not busy work.
The energy we spend doing all the mathematical problems behind proof-of-work can be seen as an investment. In the blockchain there is a mathematically certain record of all transactions that have happened since 2008. While that may not sound all that impressive think of it like this: if a single entity was responsible for building that ledger, it would have taken less "energy", but that entity would have to be trusted by every participant transacting.
With the mathematical underpinnings of proof-of-work, we are instead spending energy to create that trust model inside the currency (network+blockchain) itself. Not busy-work.
Think of it like adding microchips to paper money for counterfeit detection. That is materials and energy spent creating a more trustworthy system.
There are certainly alternatives to the BTC proof-of-work that might make for a more efficient protocol, and they might win out in the end. That should be explored. But BTC mining has value.
Building up merkle tree root, distributing the merkle tree, I agree, is like 'adding a microchip'. But what's not clear, at least to me, how does, specifically finding hashes with certain number of 'leading zeroes', helps with counterfeit detection?
More specifically, it provides confidence that some minimum amount of energy must have been used to calculate that hash. As blocks n+1, n+2, ... are added, the amount of energy that must have been used to create an alternate history of transactions since block n increases. After a certain number of blocks have been added, the cost in energy to forge a longest chain that does not include some transaction (while that transaction does exist on the original chain) will eventually exceed the potential benefit gained by "stealing back" that transaction's BTC. Note that this doesn't guarantee such an attack doesn't happen, it just guarantees such attacks would be uneconomical.
Thus, the "energy waste" of mining is really more like a security limit on transaction amounts and latencies. As the energy used--more specifically, the cost of the energy used--for mining increases, Bitcoin becomes more useful for transferring larger amounts more quickly.
I was hoping to illustrate to any less technical readers how integral the blockchain algorithms are to the security and integrity guarantees that bitcoin inherently has.
2. As in any market, the early risk-takers (who, by virtue of being early in an unproven market, are also the biggest risk-takers) will be those granted the biggest reward if they are "right" (the market/product has value).
[0 ]https://github.com/ethereum/wiki/wiki/Proof-of-Stake-FAQ
1. The process of "mining" seems like arbitrary busywork that is ultimately a massive waste of computing power and electricity. At least Folding@home was contributing to scientific research. Is there any way around this? Incentivizing a bunch of computer geeks to build massive GPU clusters and waste tons of electricity mining for coins doesn't seem like a great idea.
2. Much of the "wealth" of these coins is concentrated in the hands of early adopters. This seems to be by design (due to the increasing difficulty of mining) and is not the result of actual economic activity, but merely because those early adopters started mining first.
Can anyone (more familiar with Bitcoin than I am) comment?