MD5 and SHA-1 are no longer safe not because "most password hashes are now on the internet."   The use of salts to make passwoed hashes globally unique in fact makes this impossible.  They are obsolete because they are too fast, and too many candidate passwords can be tested against a stolen hash too quickly for comfort.

The downside of hashing is that it isn't reversible.  This is why it can't be used for all sensitive data.   You bank balance, for instance, isn't much good to either you or the bank if it is hashes, and neither of you knows what it is.