Alexia being cold, calculating and as much of a schemer as Cid is feels like the series finally found its own pace.
It creates a good dynamic of an overt domineering female lead playing the royalty romcom games vs. Cid trying to get out of her clutches so he can resume his own fakery goals.
Their fighting creates this third persona of Cid's where he's an obedient greedy dog who is slightly more forceful and prideful than he comes off publicly because he can't fight his disdain for her schemes, but gladly taking her money. Like her personality is making half of his mask come off.