Pros and cons, but I maintain that, purely apart from having arbitrary value (which, tbh, is true of modern physical currencies too as alluded to by
@Morbad), there is no other value which is produced from "mining" cryptocurrencies.
Arbitrary means the value is set by whim or decree. This applies
less to roof-of-work cryptocurrencies than it does to fiat.
As for tangential values, that would depend on specific circumstances and how abstract one is willing to go.
Claiming that cryptomining will become greener in future, well, that same green energy could instead be used for other things
Mining won't consume less energy (though proportionally fewer cryptos will be mineable as proof-of-work is supplanted by other consensus mechanisms), but energy itself will become greener in the future. And it doesn't matter what it could be used for, because it will be used for that too. Almost no one mines except where electricity is cheap and plentiful...and most places outside of Inner Mongolia or Iran, it's green energy that is cheapest.
such as air conditioning (I mention this only since it was mentioned in the article I linked).
I use the energy (hydroelectric) transformed (into heat) by my modest mining setup to heat my home five or six months out of the year. This electricity also isn't depriving anyone of anything. There is enormous surplus capacity in my area and this is reflected in the ~$0.10 per KW/h I pay for it regardless of season or time of day.
That said sure, I don't live in a situation where I have to fear that my money will get frozen or stolen by a regulatory power (legally or illegally), so I do see the value in an unregulated currency for those that do, and I accept that traditional currencies have difficulty supporting such use cases.
By the metrics of decentralization, egalitarianism, privacy, and resistance to regulation that drove it's creation, Bitcoin is an enormous failure, and any potential alternatives have been marginalized by Bitcoin's success within the framework of mainstream finance.
The holy grail would be if the "proof-of-work" calculations supporting cryptocurrencies (or blockchains in general) could be actually useful, such as protein folding.
You cannot get the benefits of a proof-of-work blockchain this way. Either your work goes toward securing the blockchain and controlling the issuance of it's value tokens, or it goes to something else. You can be rewarded for that something else, but that something else is not going to be a blockchain.
Take FoldingCoin and CureCoin, for example. FoldingCoin just rides on Bitcoin and is essentially a speculative asset that people can buy to incentivize Folding by donating to Folders who participate in FoldingCoin. It requires Bitcoin to exist and for people to buy the FoldingCoin token to give it value. CureCoin, on the otherhand, is now a proof-of-stake blockchain that ultimately incentivizes Folding the same way that FoldingCoin does.
If you don't care about or are willing to sacrifice the areas were PoW is advantageous, then you should just use a different concencus mechanism, rather than try to shoehorn work not suited to task into some centralized pseudo PoW system. Just use proof-of-stake and forget the work. Likewise, if the goal is to incentivise Folding (or whatever), there are countless ways to do this. Regardless, you'll always be competing for computational power with other networks.