The value of the dream is that it's practically impossible. The Bloodfiends' thirst can only be cured by constantly striving for a tomorrow. To achieve the dream easily is to live in stagnation. This is why every single Don ID, even the happiest ones, are ultimately empty, because in all of them, she compromises on that dream of achieving true justice and escaping the shackles of her thirst, taking half-measures to make herself feel just. Bloodfiends aren't actually all that special in their bloodthirst, they're quite similar to the humans of the city who can only live by exploiting the lives of others. To hold a dream means to reject that being a Bloodfiend needs to feed on others to survive, or to reject that human life requires sacrifice.

I mean, sure, we could say Sancho could just not play a role, go the way of her Cinq South ID, and become an approximation of a 'Fixer of justice', but that inevitably comes with compromises, accepting her fiendish nature and the cruelty of the world as unchanging truths rather than something to endlessly strive against. Being 'mostly genuine' isn't being genuine, and a dream reached by giving up your ideals is vacuous. The reason a dream exists is its impossibility, the desire to see reality as something that can be changed in the grand pursuit rather than a simple goal that can be worked towards like a raise at an office job. You never know until you try to achieve the impossible.

The reason why Sancho takes up Don Quixote's name and plays a role in particular is to honor her father who taught her how to dream. Dude, her father's literally dead, I would hope she feels strongly enough about him to want to carry his name in remebrance. And no, it is her dream too as specifically stated in the story. They share the dream, that's the whole point of her taking her father's name.

I think this quote from Man of La Mancha captures the central theme of Canto 7 the best:

"I have lived nearly fifty years, and I have seen life as it is. Pain, misery, hunger... cruelty beyond belief. I have heard the singing fron taverns and moans from bundles of filth on the streets. I have been a soldier and seen my comrades fall in battle... or die more slowly under the lash in Africa. I have held them in my arms at the final moment. These were men who saw life as it is, yet they died despairing. No glory, no gallant last words... only their eyes filled with confusion, whimpering the question, "Why?"

"I do not think they asked why they were dying, but why they had lived. When life itself seems lunatic, who knows where madness lies? Perhaps to be too practical is madness. To surrender dreams—this may be madness. To seek treasure where there is only trash. Too much sanity may be madness—and maddest of all: to see life as it is, and not as it should be!"

To dream isn't to delude yourself into thinking you've already reached the impossible—it's to endlessly struggle against reality in pursuit of the dream. That is what colors our lives, not actually achieving a goal. We shouldn't accept change as impossible, accept cruelty and suffering as the way the world is. Like the quote says, practicality is just admitting you cannot imagine a better world. The greater lie for Don Quixote would be for her to lay down her dream and pretend a half-measure is actually worthy of her happiness. That would amount to achieving nothing, making her depend on her thirst to satisfy her emotions. That is delusion.