Why is a decentralized public ledger important?

"Traditional monetary systems rely on centralized ledgers maintained by banks or central banks, which can provide efficiency and security but also give substantial power and profit to the record-keepers. A decentralized system distributes record-keeping across a network of individuals or institutions while allowing everyone to share and inspect the same ledger. The system must prevent any one participant from tampering with the records and must provide incentives for participants to maintain the ledger honestly."