Who or what closes questions here on the Physics Stack Exchange site?
None of my questions are "homework" questions, and I wish whoever closes them would actually "read them more closely". Is it some dumb AI algorithm or what?
On physics.SE, questions are closed by a voting process. Voting is permitted for members whose reputation is $\ge 3000$. Questions can also be closed by moderators$^*$ and other high reputation members$^*$ (for example, a member with a "gold" tag badge - see this). It takes three member votes to close a question.
AI is most certainly not involved in any voting processes.
Whether or not a question asked was actual homework (e.g., assigned by your teacher/professor) is not relevant. See this and this meta post for more information. Well thought out and researched conceptual physics questions are most desired, whereas those asking about a specific computation are not usually desired.
Your assertion that members do not read questions to determine whether or not to close a question is incorrect. This is why experienced SE users are awarded the close privilege.
$^*$ In such cases, other votes are not necessary.
I'm one of the persons who voted to close your question on spin direction.
Honestly, your question is confused. There's no concept here. One does not arbitrarily choose $\cos\theta$ or $\cos\theta/2$ or $\cos^2\theta$: you just correctly work out the math, as done in details in multiple textbooks and I'm sure on multiple websites as well. In its current form your question is like asking: what is underlying physical concept to compute the probability of rolling two dices and getting the total (die face 1 + die fact 2) to be $7$?
The difficulty is that, with some (minimal) amount of research, your question would become "check-my-work" or an homework-like questions because it is precisely the type of question that one would ask in an assignment.