How active should professors be in writing papers with their students?
Writing "good" papers is an integral part of being a good academic, and therefore it is, in my opinion, something that supervisors should teach their students. 

This means you should be active in teaching them how to write, and less active in the actual writing itself.

Struggling is part of any learning process, provided they are struggling with writing, and not with your reviews. The best you can do is to provide the student with clear goals of how the paper should look, how it should be structured and what it should contain. Looking back at my own first papers, I usually started writing before knowing exactly what the bottom line, e.g. the take-home message, should be. Discussing a plan of the paper, both with regards to content and the writing process, with the student before letting him/her write it is probably a good idea.

When reviewing the manuscript, I think it's important to provide clear, consistent and constructive criticism. Specifically:


Clear: If you don't like a sentence, paragraph, figure or table (don't forget these latter two!), make sure you tell the student exactly what you don't like about it. This may require putting intuition aside and thinking through why you're not happy with it.
Consistent: Avoid editing ping-pong that lead to the same paragraph being re-written 20 times back and forth. It's probably a good idea to keep copies of previous iterations with your own comments. This also helps the students if you can tell them they've done a good job fixing things from the previous iteration.
Constructive: This is kind of obvious, but I can't be reminded of it often enough.


Deadlines are a bummer, but they're as much part of the academic process as the writing itself, so the best you can do is to teach your students to prepare for them adequately, i.e. plan ahead.

Addendum

As for authorship, in my opinion, teaching a student to write a paper in no way qualifies as co-authorship. It's part of your job as an academic. Co-authorship is something that arises out of having contributed significantly to the contents of the paper.