From the Wiki article Cassius linked:
“She is often viewed as having provided Romans with fairer taxation, improved education, assisted the poor, and created tolerance in Roman society.”
“While Plotina was a widow, her best-documented act took place. During the year 121, while the emperor Hadrian was inspecting the provinces, Plotina engaged him in a series of letters to discuss who should be the new head of the Epicurean school of philosophy in Athens. She petitioned for a change in the law, so that Popillius Theotimus, the acting head of the school, could become the official head; in response, Hadrian agreed with her argument, and the relevant letters were preserved in a series of inscriptions. Freisenbruch notes, ‘In stark contrast to her passive anonymity in the literary record, this inscription from Athens recasts Plotina as a highly educated woman, active on behalf of causes close to her heart and with the kind of access to the emperor once enjoyed by Livia.’"[11]
A powerful, confident, intelligent woman, then – active behind the scenes.
Re: rumors surrounding her role in securing Hadrian’s succession:
“It may also reflect male Roman displeasure that an empress – let alone any woman – could presume to meddle in Rome's political affairs.” https://en.wikipedia.org/wiki/Trajan
Ah, how the times, they do not change!