It kind of irks me when people talk about Li Zhi like he's such a sweet and meek person and that's it. Like, no, that's a master manipulator and actor and he got you too.
Li Zhi was literally the one who orchestrated Li Tai's plan to depose the Crown Prince. (Li Zhi's bodyguard asked if they should dispose Chen Xin, which means that Chen Zin knows Li Zhi's hand in all this. Further, Chen Xin going back to the Crown Prince to tell him of Li Tai's role literally doesn't make sense unless Chen Xin had a powerful backer that could sneak him in + could benefit from the Crown Prince wanting revenge on Li Tai.) Li Zhi did this without Li Tai even realizing it.
Li Zhi is constantly calculating and thinking about how to use people. When he learnt that Gaoyang and Yuanzhao were going to the burning temple to save Bianji, he still had the presence of mind to order that this info be leaked to Li Tai, because he knew Li Tai would definitely come to save Yuanzhao too. This is someone who's used to thinking about all sorts of possibilities at all sorts of times. He's an instinctual schemer.
Quite frankly, the reason why Li Zhi doesn't have as many dramatic scenes with Yuanzhao as compared to Li Tai is because:
Li Zhi simply would never get caught in a dramatic situation where he would kill a general in front of witnesses to save Yuanzhao. His style is to do things from the background, via indirect methods. The most Li Zhi has put himself on the line for Yuanzhao was to use his own marriage as a bargaining chip. (Which, don't get me wrong, is still a pretty big deal, but it doesn't run the risk of being stripped of your role. And still benefits Li Zhi politically.)
Li Zhi has way too much control over his composure to do the thing Li Tai does where he obviously smiles and loses his cool and then tries to shut that down and act cool. And also Li Zhi whole persona doesn't involve acting cool and impervious in the first place -- it's quite the opposite really. (He clearly acts dumb and guileless in front of everyone who isn't his bodyguard.) So when Li Zhi does get flustered by Yuanzhao, the contrast with his usual self is not as glaring and dramatic.