Let's say you have a shared database which does support the following functionality (which you mentioned):
A) Easy to revert transactions afterwards
B) Shared (in some fashion)
C) Supports restrictions, authentication and the all the regular stuff
I'm not very fluent in various databases but I guess you can find a database which supports those functionalities.
Then consider the following points:
1) How easy is it really to revert transactions in your database? Whose job is it? Is the control centralized?
2) Who admins the database? Who controls access? Who sets it up (or starts it)?
3) How do you control how much processing power each user gets? If it's unlimited, it will be abused.
Ethereum answers all of these problems: 1) Longest chain is deemed to be the canonical chain and other transactions get reverted. 2) There are no admins, the only setup was years ago when the blockchain was started. 3) Gas.
The public Ethereum blockchain is the best option, but private blockchain also supports all the same functionality - it is just typically a bit more centralized.