I also think every Scouter should have the chance to be on staff, too. Here's why:
You learn more. Wood Badge has been described on multiple occasions as drinking from a fire hose. There are so many skills and principles taught, demonstrated, and experienced that I'm not sure it's possible for any normal person to pick it all up the first time.
Not only do you learn more of the leadership skills being on staff, you actually have time to study them. As a participant you have one week (or two weekends). Sure you have up to 18 months to put them into practice by working your ticket, but unless you take really, really good notes and study them you're probably going to forget. When you are on staff, you are working on presenting some of those skills. You have months where you need to study the course with all of the material at hand. You also get to sit through all the presentations again and learn things you may not have picked up on the first time. All that repetition drives home some of the messages that are missed or forgotten as a participant.
As a participant at Wood Badge, you get to experience in a patrol setting many of the concepts being taught. You actually go through the stages of team development. You practice listening and communicating. You may get to do a bit of conflict management. You are using the steps of project planning to develop presentations. You do an assessment every day, and you are constantly thinking about your vision. The experience is an essential part of the course, as it helps you better understand the principles being taught.
As a staff member you also get to experience some of those things in your associations with the other staff, but you also have a greater opportunity to observe how others are experiencing those things. Several times I found myself watching a patrol (or an individual) go through a challenge and thinking that they could apply the skills learned in a presentation they were just taught. You have a greater opportunity to see how those leadership skills can and should apply, and since you have a greater knowledge to back it up, those experiences can be more meaningful. You get to see how the course is put together and that everything in it teaches something important.
Many have seen the difference made by one Scouter who attends Wood Badge and works his ticket. Imagine what would happen if that Scouter had the opportunity to do the same thing every year (or every other year) after that.