Why would a singer want to use a corset or a waist trainer in their training?
I find that having the gentle, elastic resistance of a corset/ waist trainer can help me to find a better appoggio, or relationship between my diaphragm and abdominal muscles in my breath support. I will sometimes use these devices for a few minutes at a time to help me establish that appoggio; for my studio, I may offer the use of them to a student to help them prevent collapse.
Once a young singer has learned to take a deep abdominal breath and has abandoned the high, chest breathing, a new stage in development begins. Often, a young student will inhale and immediately push their abdominal wall in to support their air. I use the waist trainer to help them keep their abds out as long as possible to resist this new collapse and squeeze.
I would recommend the following waist trainers as being tested and true:
Trainer/back brace : $30
Three strap trainer: $45
Single strap trainer: $15
I hope you enjoy playing around with these yourself and in your studio!