She lends the PC and others power to accomplish goals they have in common
Goals that she effectively forced them to have. And I don't mean in the "she tempered you" way or even the "she hid knowledge from you that may have changed your opinion" way, but rather the "the state of the world and your very being that she is responsible for creating leaves you no choice but to align with her" way.

Her duplicitous context doesn't make a difference
I really feel like it does.

doesn't compel service
Minfillia seemed extremely compelled. As well as Middy. And Ryne and all that on the First, they never had a choice.

has to act through mortals by granting them power and hoping her read on them is right, and doesn't take that power away should her read be wrong.
She does ignore their plight when it suits her though. Urianger had to effectively barge into her room and poke her in the eye to get her to help the First.

namely stopping the Ascians' genocidal / omnicidal plans
I'm just going to say it - Hydaelyn's status quo for the world is infinitely more genocidal than the plans of the Ascians. She is responsible for more death than they could ever dream of causing, every living being that has ever died on any of the shards or the Source can ultimately owe that loss of life to Hydaelyn.

She exists solely to bind Zodiark
This is extremely debatable. Hydaelyn taking up her position in the Lifestream, hearfeelthinking anyone who awakens the Echo regardless or whether they have anything to do with the Ascians or not, bargaining for Midgarsormr to die, give up his aether to her, and eternally enter her service guarding whatever is beneath Silvertear, she does more than only keep watch on Zodiark.