Surely we can adjust the protocol to say "has found 8 0's and signed the value with one of these private keys". Attacks become based around the security of those keys - as its a private chain anyway, do we mind?
Why bother with it at all? Authenticated database sounds like.. postgres.
Because it's distributed (NasDaq going bankrupt won't kill it) and all changes are in the open (no rogue employee stealing your shares). Sure you can achieve more or less the same thing with a relational DB or by drawing sticks on a piece of papyrus.
So you think Bitcoin is the first distributed database? No. There is no reason for a private blockchain to exist; it's a nonsensical idea.
This seems to be a case of "you don't understand" - what sources / reading would you suggest covers this issue ?