No, centralized databases proved itself untrustful as the concept of being centralized holds the one and only source of trust, and if it gets compromised (and it will, 0day using viruses will appear periodically) there will be data loss/exposure, varying from non-zero to 100% (assuming there are backups made, and level at which data is encrypted).

Blockchain can eliminate this problem, as it gives extreme level of trustfulness to database current state, due to multiple trust nodes over the network which one by one sign trustful transactions.

However, your point is valid, because there are multiple nodes which hold same data state and all transactions being publicly available, the privacy is to be concerned about. There are ways to make nodes do extra steps on assuring transaction stays private and does not expose critical data. But the certainly we can say that, centralized database has definite advantage over blockchain (yet) at this point.

You can read this article as it has points I gave in this commentary: http://www.multichain.com/blog/2016/03/blockchains-vs-centralized-databases/