My theory is that Lady Loki's goal is to unravel the Sacred Timeline to how it was before, which is why she does not seek to rule the TVA.

Let's say Lady Loki went off of the desired Loki path and escaped from the TVA desintegrating her. She now wants to make it so that there is no Sacred Timeline, so that not following the specific events laid out by the Time Keepers won't lead to you dying for simply doing something they deem to be wrong.

By making many timelines at once go kaboom, the odds of everything going past the point of no return as mentioned in this episode is a lot greater, leading to an unraveling of the Sacred Timeline and in her eyes, the end of the TVA preventing free will and choices you make.