BioShock 2 revealed that Andrew Ryan had a secret prison to throw people into when they disrupted his control over the city. And more than once he decided he would burn it all down rather than let someone else win.
It may have masqueraded as anarchy, but the system was still rigged from the start. There was always a ruler.
Did you play the BioShock infinite dlc? They had a strange retcon where the Lutece twins approached Fitzroy and instructed her to appear to be a monster, specifically so Elizabeth would feel like she had to kill her.
It was a strange choice, because the remaining revolution was pretty blatantly horrible without her either way, and I’m not entirely sure that’s how this sanitized version of her would want it to go.
The politics of BioShock are not all that deep in the end. They’re mostly just a setting so they can tell a story of someone forced into a role without understanding it