I feel like you are mistaking the forest for the trees.

I am not sure what you mean by this.

My point isn't that by introducing humanities as mandatory, we will somehow magically transform our society into a utopia.

Sure. But you seem to be assuming at least one of the following:

• Forcing STEM students to take humanities exams will make them better at evaluating social utility of their professional decisions.
• Forcing STEM students to take humanities exams will make them evaluate social utility of their professional decisions.
• Forcing STEM students to take humanities exams will make them use the aforementioned evaluation in a way that would improve social utility, compared to how things are now.
• Forcing STEM students to take humanities exams will increase the frequency with which they can make the aforementioned evaluations, even as junior professionals.
• STEM students are not forced to take humanities exams enough.

That is quite a few assumptions, and, considering that humanities (and art) specialists do not seem to be significantly less ghoulish than STEM specialists, I do not think that any of them have a good basis.

Also, how much of STEM curricula do you want to replace with humanities courses? Just one semester of a bunch of disparate disciplines is not going to give them any useful skills, so the courses have to be more thorough, and the students will come out knowing less about STEM fields that they come to study.

My hope is basically just that it might change things for the better a little. Just because people are generally terrible doesn't mean we cannot work for making them better even if it is just a little bit.

Sure, but how would that improve things? What are the expected mechanisms that would cause things to change for the better? Humanities (and art) do not seem to make people significantly less supportive of things like genocides, colonialism, and capitalism.
What seems to be a better alternative is not forcing humanities and art courses on STEM students, but attempting to instill them with relevant worldviews - ones which oppose the likes of the aforementioned atrocities.

I believe that by educating them we might hope that at least a few might make better choices or not.

Humanities education doesn't make humanities specialists not be awful. Why assume that teaching less of it to STEM students - at the expense of the knowledge about their fields of specialty - would make them either do more of social utility evaluation, or do that evaluation better, or use that evaluation more frequently and for the common good?