It's a terrible way of doing that, and it isn't even necessary to produce an immutable record of transactions. Seriously, spend some time thinking about other models for distributed transaction records.

Blockchains are designed the way they are to prevent governance and oversight, meaning, if someone scams you or steals from you, there's no way to get your money back. "No backsies" is the most fundamental principle of their design.

Isn't it subjective immutability?

Your transaction might disappear from the history if the view changes to have some other branch be the accepted one

The PoW on top of a tx produces immutability in the sense of a minimum cost imposed on a rewriting of that tx. If no attacker is willing to bear that cost, then the objective longest chain rule (i.e. most cumulative difficulty) will preserve the history up to that tx. Without PoW you have no objective way to determine the true history.