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 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.