Colleges expect teacher to provide letters that fairly reflect their opinion of the student.
Writing a reference letter is not an academic function, it is a management function. Originality and authorship are unimportant in a management document, what matters is that the right level of person signs to confirm the information - how suitable is this student for this or that new opportunity.
If an intern in a widget factory writes a letter saying that our widgets are indeed suitable to manufacture blodgets, it is perfectly appropriate for the boss to edit the letter and sign and send it without authorial credit to the intern.
Someone who writes every letter from scratch is either nuts or has too much time on their hands.