The proof of work aspect of a lot of crypto is the thing that never made sense to me. It's so pointless. I agree with the rest of what bitcoin offers but why use proof of work?
So cryptocurrencies can't exist without something to validate it.
All fiat currency cannot exist without some sort of validation.
The very point of fiat currency is that it holds no intrinsic value (aka the material the object is made of isn't valuable, or nominally low compared to the amount it represents), but that some sort of central authority grants it value, and that guarantee is what allows us to exchange it with each other for goods and services, because at the end of the day the requirements for you living in that country (aka paying your taxes) can be met with that currency. Americans buy and sell things with US dollars, because US dollars is what's needed to pay your taxes in the US. Some people in the US will accept other forms of currency (like Canadian dollars, or mexican pesos), because "those" governments have offered guarantees to it's value, and your ability to exchange that currency to USD grants it value.
Someone also has to keep a record of these transactions, because now that the money itself has no inherent value, the idea of having intangible value exists. Someone needs to keep track of how much "money" you hold, even if you aren't "physically" holding it.
The problem that crypto evangelists put forth, is that there was no good way of universally sending cash from person to person without dealing with currency exchanges and exchange rates, or lack of support for certain countries for these money transfer services, and political interference making current fiat currencies inherently untrustworthy (in their eyes).
These central authorities can simply print as much cash as they want, or arbitrarily decide to no longer recognize previously printed bills, and you, as an individual, have no control over that. Western Union and other wire transfer services have too many fees and take too long. The internet is becoming more and more ubiquitous world wide, but access to financial services still lag behind. Banks could simply decide to fuck off with the cash you entrusted them.
So why not make a "digital" currency. Some universal unit of value in which no individual holds control over. Free from political borders, transferring should be seamless and painless. By dividing the consensus amongst a decentralized group, it should be immune to the whims of an individual government manipulating it's value. But how do you impart the same level of guarantee that a central authority does, if there is no central authority by design? How do you ensure transactions are filled, that people aren't just scammed out of their money? That someone doesn't just decide to "undo" a transaction when no one person has the final say on what the record is? How do you achieve "consensus" on what the "truth" is?
Proof of work. It provides the validation required to make a "currency" by tying all transaction history to a system that would be extraordinarily difficult to overthrow on your own (in theory). Everyone is working to prove the same transaction history. If you attempt to provide a record that doesn't mesh with the rest of the group (the majority), you're rejected. The only way to surmount this is to have control over 50% of all the workers, so that way your history (as you decide to write it) is the "correct" one. The work is tied to arbitrarily difficult equations that need to be solved. Having to control 51% of the workers in a decentralized system of increasingly difficult (and time consuming) equations of a sufficient scale should be a fairly insurmountable task.
But just how "640k ought to be enough for anybody" was wrong (which is not a real quote btw), PoW was not a future thinking design. The scale in which it grew was exponential. Because of mining pools and the ever-present risk of a 51% attack, an arms race begins. I don't think they considered the idea of ASICs when coming up with this. Because the generation of wealth in Bitcoin is directly tied to the work going in to maintaining the network, there's always an incentive to add more workers to try and exact as much of that wealth for yourself as possible (so long as the cost of building these ASICs is low enough to recoup your costs in rewards from mining in a reasonable timeframe).
So how do you solve that?
I've seen a lot of support for Proof of Stake, where consensus is now achieved by making those who actually "hold" the currency the ones who validate the network. In theory so long as no one owned more than 51% of the total supply of the currency, it should achieve the same result as PoW (aka no one person gets to write history). The problem (at least from what I see), is that many of these PoS currencies also tie rewards to this. So the more currency you hold, the greater "reward" you can get by being a larger percentage of the overall total. It just encourages hoarding of wealth rather than actually, you know, using it, and almost codifies the idea that the rich get richer (and do it faster than the poor). It's also irrelevant when talking about Bitcoin, because Bitcoin can't change. It's going to be PoW forever.
And Ethereum, I'll be genuinely shocked the day it actually moves to PoS. They just keep pushing it back over and over, I think they know there's a disincentive to doing so.
So in summary, PoW exists because it's the "simplest" means in which to achieve what normally a central authority/banks would provide, while ignoring all the ramifications of what that actually means outside of the currency itself (like power or material consumption). PoS, while gaining in popularity, is held back by it's being codified that those who hold the most wealth grow their wealth faster than you (and those with vested interest in PoW due to supplying or owning the equipment for it not wanting things to change)