I don't know if "rousing" is the correct word - a running theme I've seen with Lilith is that she has the ability to make people embrace their own desires. For the people of Nevesk, it was enticing them to act on their hatred for the priest. For Vhenard, it was having her act on her desire for knowledge, even at the cost of losing Neyrelle. For Ariadnah, while less clear cut, the implication (at least for me) is that Lilith led her to act on her dark thoughts (her social Darwinist view towards the glenfolk). As in, she genuinely believed that culling the weak would work in the long term, but moral inhibition prevented her from acting upon it.
As for the idea of structure vs. rebellion, well, if you're saying that the story would be better if it involved Lilith inciting rebellion against the Cathedral...well, okay, sure, I haven't completed the game, so I'm not in a position to speculate on that counterfactual, but I'd make the following points. First, that would already be a repeat of the Sin War in a sense, where Lilith, directly or otherwise, formed the Edyrem as a battering ram against the Triune and Cathedral (yes, her deception was revealed, but Uldyssian ultimately continued the crusade for his own reasons). Second, the dichotomy between order and control is already well established in the themes of the game. Inarius, true to his nature, is draconian, and so is the Cathedral of Light, but it's draconian control that has a function, considering the protection that the Knights Penitent offer against the horrors of the world. It's arguably telling that it's even hinted that the Cathedral has waged war on the Zakarum (if you're further in the game than me, maybe you can confirm if this is true or not). On the other hand, everything I've seen with Lilith allows for free will, even if that free will results in heinous things. It's part of why I don't agree with the notion of Lilith being no different than the Prime Evils in that:
1: The Prime Evils only ever saw humanity as a tool for their own ends, Lilith appears to have genuine affection for humanity, considering that they are, in a sense, her 'children.'
2: The Prime Evils have corrupted people directly, as in, forced them against their will. Even if we confine this to the games and nothing else, Diablo corrupted Leoric, and has possessed Albrecht, then Aidan, then Leah. Mephisto corrupted the whole Zakarum faith, and possessed Sankenkur. Baal possessed Tal Rasha. The TL, DR version is that the Prime Evils have outright forced people to act in service to their own goals. Lilith, at least of what I've seen, gives people the choice of acting on their impulses. Yes, Lilith has possessed people in the path (e.g. Serenthia), but in the specific context of D4, her M.O. is pretty different.
3: Lilith's grief over Rathma. Yes, I'm including this as its own entry, because there's no way, under any circumstances, a Prime Evil would ever feel grief over the death of a child. If you don't believe me, look at what Diablo did to Leah, or how it's well established that Lilith "felt her father's hatred."