I'm sure those proofs at the time were novel to the student but obviously not the professor who assigned the problem. That's how the student learns.

They have to be novel in my experience.

I have a BS in Mathematics from a mediocre school (University of Arizona) and exams were always "prove this fact (which you have never heard of before)", never "what is the proof of XYZ theorem (which we studied)"

there is so much room for questions, it's quicker to write the proof than to search an answer. And a readily found answer would, for undergrad, less likely be in proof form, or too distinct for specific topics later on. And the instructor might become suspicious and interogate you, in which case, if the material helped you to understand, that's the point.