There is also a famous critique of Rawls-type liberalism in Robert Nozick's Anarchy, State, and Utopia, which is in essence a libertarian text - but also a keystone of political theory in recent decades.
Nozick says you cannot assess justice or fairness by looking at a society in a "time-slice"- the situation at a single point on time, regardless of how that came to be historically.
He gives an example of Wilt Chamberlain, a famous basketball player at the time. Suppose everybody in society starts equal. But it turns out a lot of people are willing to pay a dollar to see Wilt Chamberlain play basketball. They choose to do so voluntarily and with some enthusiasm.
Before long, Chamberlain is much wealthier than anyone else - and all because of people's free choices. Nozick asks in what way is this unjust or unfair? In this case equality at a point in time is not necessarily "fair" or unfair. It depends among other things on what has already happened. Our actual history matters. Rawl's original position does not work.
In real life, of course, we do not start equal. But even in its own terms, "fairness" is often controversial.
Maybe we need to think more about what people actually want in practice, rather than thinking about procedural justice alone.