This is a depressing thread.
It's not true at my institution. In fact, I am specifically prohibited by our Honor Code from deciding to just let a student rewrite a plagiarized paper. I'm required to send it to the Honor Court. The only exception is if the student has attempted to cite properly, but made mistakes. In those cases, I still have to send a letter to the dean, explaining the circumstances and my preferred sanction (grade deduction, rewrite, etc). The dean doesn't have to accept that, and if a student has more than one such letter on file, he'll tell me to submit the work to the Honor Court.
The conviction rate, by the way, exceeds 95%, and the minimum sanction is failure of the course.
Does no one else work somewhere with a vigorously enforced Honor Code?
Are you at Virginia Tech or something (you don't have to answer that)? But no, there aren't many institutions with a vigorously enforced honor code. Most institutions want to cover-up and ignore instances of academic dishonesty. At my current institution, most faculty feel confused and powerless in the face of plagiarism because we have no clear cut policy. If you don't have a predictable dean, you are pretty much lost. My current dean would back me on any reasonable punishment for this. In fact, I usually make my punishment less than the dean would support. I have had students appeal my decision to the dean and then come back to me with a written apology asking if they could have my punishment instead. I love my dean.