You see it coming from a mile away every time because a truly emotionless character would be boring as fuck.
I would disagree with that sentiment. A truly “totally objective, emotionless, logic based” character can work, but the author needs to understand how AI, analysis and algorithms work and the limitations and quirks of such AIs. I am no AI scientist, but in my field of study, Economics, we do a lot of empirical analysis, which could be supplemented with AI. In Empirical Economics a lot of policies are analysed, and we are able to achieve objective results of those policies, but the evaluation of said results cannot be done by purely objective means.
As an illustrating hypothetical, there is a policy that affects two groups of people, A and B. The policy subtracts income from the A group and gives it to the B group through a transfer. Should you implement the policy? In most cases, unless you have a situation in which the policy makes both groups worse off, you cannot objectively evaluate the policy, because you need to assign welfare weights to these groups.
Further AIs and algorithms can be objective, emotionless and logic-based but still be wrong or biased, because data can be biased, incomplete or incorrect. It’s why collecting good data is so important for science. Further, why in Economics there is always the question of intuition. Certain result are more plausible than others and those results that run counter to intuition need to be double-checked.
All of this could be explored in such an AI character.
I am not even talking about an AI with emotions that acts against them. I am talking about an AI has no emotions, but acts on pure logic, and the goals and axioms given to it by its creators. You can explore all sorts of questions with such an AI.
As for your examples, I know the sapient AI trope is used very often. I was much more “annoyed” at you stating that an emotionless AI character would always be boring.