Even as an Esdeathfag I can't believe you missed the point of her character this hard: she loves to fight, and she loves nothing more than to fight.>But muh Night Raid tho
She joins and... then what? Sure, she gets to fight for a while and then? The emperor is deposed... and then what? The anime ending seemed to imply peace and freedom for all.
Now compare if she sticks with the empire (remember, she's literally the only reason it's still standing). The empire is corrupt and she knows this. Everyone fucking knows this. That's why there's no short supply of rebels willing to overthrow the emperor, ie. meat for the slaughter.
What Esdeath cares about, perhaps more than about Tatsumi, is what side allows her to kill the most. As it stands, that's the empire by a longshot.