Why the restrictive style in academic writing?

I think it has to do with both the strength and clarity of what you're saying. As someone else said, first-person makes the essay sound subjective and opinion-based. Obviously, your essay is still subjective to an extent without the first-person, even if it's well supported, but seeing the first-person phrases just emphasizes that to people. Too much passive voice, especially where it can be avoided, also tends to make your essay sound vague and weak. Active voice just has a stronger and more declarative sound to it, and it helps cut out unnecessary words in many cases, which makes the writing more concise and easy to understand.