She doesn't have any lofty ambition.
Sure she does. I mean, yeah, at the moment her lofty ambitions are just 'do what other people to tell you to do', but they're still something.
A lot of the Arrancar in Bleach seem to suffer from this... not a lack of ambition, exactly, but a lack of anything to
do. This leads them to a kind of ennui, and from there stagnation- because when you've achieved the kind of power that can't be matched by many in Hueco Mundo, and you're no longer ruled by a constant all-consuming hunger that needs to be sated lest you fall back into a mindless state, what is there to
do? Not much, really. Kill some minor Hollows, maybe some bickering with other Arrancar. And then... more killing. More bickering. Maybe pick a fight with another Arrancar, kill them, and no longer have someone to bicker with. Kill some more Hollows. Etc, etc. Grow more powerful, but for what reason? To do what? So you can kill other Hollows easier?
Avoiding that kind of ennui
is a lofty ambition in itself, even if not actively considered as such by Nemo. It also requires that Nemo constantly be doing stuff, and it's unlikely that Barragan will always provide tasks like this to keep her occupied.
Does that mean that you have to pick the Butcher King as the place to make that kind of stand? Nah, probably not. Sure, it's interesting, but it's also not likely to last- they're already having trouble finding Hollows to kill, and eventually internal strife will tear it apart, if the Butcher King isn't killed first (signs of such are already showing). And it's not like two low-ranking natural-born Arrancar will be able to form any major societal shift in the Arrancar. He's a novelty; something interesting, but also something essentially useless right now.
Pick and prod at it, sure, Nemo might keep it in the back of her head, sure, keep the Butcher King as a character for Nemo to bounce off of, sure. If I don't have to leave tonight and the Butcher King doesn't get killed next update, I might write an omake about it, see what it can lead to. But make it a major thing this early in the quest, with nothing in characterization to bounce from and no real idea for where to take it? Probably not the greatest idea, more likely to lead to Nemo being eaten than anything.