Sure, they can do it for them - but the purpose of college is not to write papers. The papers are so that the students can demonstrate that they understand the subject and that they have "learned to learn". If an LLM writes it for them then they haven't proven anything other than that they can prompt an LLM. Which is great if your college degree is for "LLM prompting", but not much else.

I hope people that use LLMs to generate papers fail in other tests, else the value of a degree will be reduced to nothing - it's already suffering from a lot of "inflation" due to lowered standards and oversupply. (The lowered standards are because graduation rate became a metric and a target)

"but the purpose of college is not to write papers. The papers are so that the students can demonstrate that they understand the subject and that they have "learned to learn"."

That depends on the perspective. In theory, that is the correct view. To many, the degree is just a piece of paper used to gatekeep jobs.