Enshittification happens due to greed and power; It's just the process of removing the false mask of mutually-beneficient business that Capitalism uses to hide its true self.

First you make users think you're beneficial to them, so they get locked in,

then you make businesses think you are beneficial to them, and get them locked in,

then you give up that facade and admit you don't care about benefitting anyone but yourself.

You can enshittify something even as an individual; it's not being publicly traded that makes it easier or more likely, it's that being a large enough business to be able to successfully enshittify without losing all your customers probably means you're publicly-traded.