According to literature cryptocurrencies can help avoid double spending and generating of fake currencies into the system. The blockchain technology which serves as a distributed ledger system for all transactions of bitcoin prevents double spending and also because the honest nodes on the bitcoin network outweighs the attacker nodes, the nodes within the network only confirms true transactions unto the blockchain other than any suspicious transactions.
Also, because the blockchain technology is an open source decentralized network everything occurring on the network is very transparent and therefore people can just make their own currencies into the system.
Bitcoin is PoW based as an implication of PoW and these are all the pros that exist in Bitcoins. The details you mention belong to PoW and blockchain technology is not limited to this only.
Concerning your question, blockchain technology can be used to prevent fake fiat currencies and many other financial problems as it can help to create cryptography based currencies that are completely digital. These crptos will not only ensure decentralization but transparency, privacy and security as well.