Pros and cons of PoW.
The biggest advantage of proof-of-work algorithm is that it work and nobody can argue that it works. Proof-of-work has been working on the Bitcoin blockchain from the launch of the network in 2009. Since then, the network has grown in popularity exponentially, gained mass attention, had the coin going in price from under a penny, with a person trying to buy two pizzas with ten thousand bitcoins in 2010, to almost $20,000 and people selling historic mansions in the Upper East Side neighborhood of Manhattan in New York City for cryptocurrencies, yet proof-of-work has been working all this time. The genius of the algorithm is that the more people use a network that uses proof-of-work and the more miners the network has, the more secure the network will become. With Bitcoin network, this means higher difficulty of mining and increased hash rate (the speed with which hardware can generate hashes required to mine blocks of a blockchain network that uses proof-of-work).
You can see what has been happening to the Bitcoin blockchain’s hashrate by looking at the following chart: https://blockchain.info/charts/hash-rate
There are two big problems with proof-of-work. The first problem is that running mining equipment on the proof-of-work networks requires a lot of electricity. According to an article in Motherboard from November 1, 2017, in 2017 one transaction on the Bitcoin network required as much energy as a typical American home burns in about a week. An article in the Guardian had calculations according to which in 2017 miners on the Bitcoin network have burned more electricity than did in the same year an entire country of Ireland and Ireland is far from being the smallest electricity consuming country in the world. Countries such as Malta, Lithuania, Estonia, Puerto Rico, Dominican Republic and many others consume less electricity than Ireland (per country, not combined).
While some people may argue that miners only burn all the electricity they burn because they choose to do so and that the Bitcoin network and other proof-of-work networks are completely free, meaning that nobody forces miners to do what they are doing and they are free to leave at any time, the issue is that the electricity that the algorithm burns contributes to nothing. It is a way of exchange of the resource from the real world (electricity) into digital value but other than that, there is no contribution.
With proof-of-work and trying to come up with nonce that will result in winning hashes and rewards from the networks, miners are essentially playing a lottery.
It works because the network is fully transparent and the chances of winning are realistic and are distributed evenly. Practically speaking, this is similar to playing a lottery 9 times where you have to pick one of three outcomes. Statistically speaking, a chance of picking the right outcome out of three is one-third in every draw. This means that if you keep playing long enough, you will win as long as the lottery is an honest and legitimate lottery.
This is exactly what happens on the Bitcoin network and other networks. Satoshi Nakamoto made the software of the network open-source and free from the very beginning, meaning that anybody can download and inspect the software.
The comparison to playing a lottery as a part of proof-of-work may be confusing because when thinking about lottery, most people think about lotteries such as PowerBall. In the lotteries available for the public, the chances of winning from the statistical standpoint are equal to zero.
The reason why so many people keep playing the PowerBall is that chances of willing do not feel equal to zero to people who have not studied statistics. For example, when most people hear that they need to guess five balls out of 50, they could think that the chances of winning are one out of ten. When they hear that the Powerball runs from one to twenty-five, they could make the assumption that the chances are 50% of guessing the regular ball and are one out of twenty.
In reality, the changes of winning are worse than one in 290 million, which is less than the chance of dying from being killed by a shark or being hit by a meteorite.
All of this does not change the fact that while miners on proof-of-work networks are getting financial gains, the power and hardware do contribute to the security of the network but don’t contribute to anything else. This is the problem that networks such as Gridcoin are trying to solve by replacing hash calculations with solving mathematical issues for scientific projects.