I rarely have to dry clean the dress shirts under normal wear conditions. I'm guessing it depends on the GSM of the shirt.
I don't know if I would agree dry leaning defeats the purpose. Most cities have a dry cleaner and dropping it a dry cleaner is going to be faster than washing, drying, and ironing it yourself. At least it is for me. Plus, you would need to find the right kind of detergent without enzymes or whatever while traveling.
Are you saying it fell apart?