Because making a real case is too damn hard
If you look at this plan, it reduces this whole business to what's essentially an administrative process where those making the judgements are the ones running the process. It's like when you get sent to the principal's office by a teacher. While the principal may be a fair person, he can't be entirely fair because he is a part of the same institution as the teacher who sent you there, so their goals are essentially the same, and the principal has an incentive to take the side of the teacher.
Now, while the above scenario might be considered acceptable for a kid (although I've heard of enough abuses of process to doubt that), we're talking about adults here. So why are they doing it? Simple: going through the courts is just too damn cumbersome in many cases. With this setup, the ISP's and the entertainment industry get to set the ground rules upon which people are judged. The customers of these ISP's have absolutely no say in the matter, and, at the end of the day, they have no real recourse if they don't like the outcome. And even the punishments are rigged. One of them is supposed to force the "convicted" to view educational material, but that material is created by the entertainment industry, which will present its own interpretation of how copyright law works or ought to work. Do groups like the EFF and the ACLU get equal input into what goes into this material? Of course not.
This setup resembles a situation where you walk into a store and are accused of shoplifting a jacket because you're wearing one that looks like one that was recently stolen, and you weren't carrying a receipt to prove you paid for yours. You wouldn't be arrested, but your "case" would be discussed and decided by the Chamber of Commerce, and, if you were found guilty, you'd be banned from entering all participating stores, which would include most all of them.