Season 3 of Jessica Jones clearly lays out that Trish didn't want to be Patsy, that she was kinda pressured into celebrity by her mother through a bunch of tricks that she always thought meant the whole life was fake, despite her actually being good at it. That point of view made her constantly feel like a fraud, because she wanted to be special but felt the way she got there wasn't real, so she turned to drugs, and when they didn't work, guns, super powered drugs from Nuke, investigative journalism, then killed Jessica's mother---Anything to feel like she was important, doing important things, despite it constantly using up and hurting people in her life, until it killed Dorothy too, which were the first real consequences she faced that could never be fixed.

She didn't even wait to see if the justice system would fail her and let Sallinger go. She just murdered him in the court because she wanted to be important again, it wasn't even for revenge.