It starts with sanitation issues, so no recipe book can safely recommend it. But let's say your name is Fartographer and you really wanna try this with dishes in your parents' dishwasher in high school; you'll discover the following four issues:
A) Dishwasher detergent is really gritty as to scrub the dishes with jets of water. This makes the water erode thin materials like foil really quickly and easily.
B) After the initial rinse, dishwashers fill the bottom of the unit with water and then recycle that water. Any chunks of food or other materials eventually get cycled and shot out through the jets, which can further rip your foil.
C) Once your dirty dish soap water breaches the foil, your fish tastes like soap and is peppered with old washed-off food, and the cooked parts of the fish are shredded.
D) Because of everything listed above, foil pieces and fish chunks will join your dishwater and be cycled through your dishwasher. Most dishwashers aren't built to handle large chunks and pieces of metal, so this will likely clog the sprayer arms and then the drain and you'll have to spend days disassembling and cleaning your parents' dishwasher.

Of course, all of the above can be avoided if you use thicker foil and more of it, but then your fish doesn't cook all the way through. So, best if you don't run your dishwasher salmon with your dishes, better if you don't cook your salmon in the dishwasher.

Edit to add: this cooking method was first popularized around the time that people were putting shit into jello or mayonnaise and marshmallows on everything and then serving it at their large dinner parties. If you're hosting 24 people and cooking a salmon fillet for each person, running the dishwasher for a cycle starts to make a lot more sense. Add in that everything needs to have some craaAAaAzy gimmick, and "surprising" everyone that you cooked salmon in the dishwasher becomes the best method.

You can. It literally says so in the wiki article. You shouldn't, obviously, but you shouldn't even try to cook fish in the dishwasher in the first place. But if You are willing to try it, go for the full experience. As we say in Poland "If You said A, say B..."