First off, if you just let first graders write whatever it would take the teacher way to long to sort out and explain what was wrong. You're describing a college class,or at least a somewhat advanced college class. There's no way to try and teach a classroom with everyone going in their own direction and no guidelines to adhere to.

You need to site even common knowledge because you think everyone knows because what everyone knows can be wrong. There's some exception depending on the specific paper and audience, you don't need to cite a source on what evolution is when you're writing to biologists because you know they know, but a claim about what Christians belief, which you may have learned growing up, needs to be cited because there are hundreds of interpretations, you can't know what the audience has going in and you may just reinforce stereotypes. Your point about facts and logic versus chains of evidence and thinking is absolute gibberish, I have no idea what you mean. Strongest guess based on the vibes around facts and logic is you just mean using sources instead of your own point. That's already built into writing a paper because if you just say what others say and never voice your own argument you probably did the assignment wrong.

Most citations and pretty easy to make, plus teachers and librarians will almost always help in my experience. I've never seen a citations style you need to pay for.

Learning to consider sources and what exactly someone is saying and why does more to fight capitalism than aid it. School classes that create office drones are the ones that fight critical thinking, this is one of the only techniques that actually makes some people think about what they are reading.