You are conflating different issues here. Income equality is not actually due to free markets. Monopolies in free markets do emerge but in the socialist system

You are conflating different issues here. Income equality is not actually due to free markets. Monopolies in free markets do emerge but in the socialist system (defined as government providing services in return of taxes other than infrastructure, defense and health+education safety nets) the government is defacto army-enforced monopoly. And yes, no system is perfect. You have perhaps not heard about how governments all over the world have enriched themselves by monopolizing everything from entire industries, natural resources to sports teams while promising better services to the public (spoiler: didn't work out for vast majority except for Norway). You have perhaps also never been involved in government grants and contracts to see first hand how extraordinarily inefficient, bureaucratic, slow, irresponsive, unmaliable, frustrating, insensitive and far behind the time these entities are top to the bottom. To anyone dreaming of a socialist system as salvation, I would highly recommend taking up a year or two of a government job to see how it actually functions and what are your chances to improve it even a tiny little bit.