OUCH.. NO souvenirs at all?
I limit my children's to one a day. There's a psychology behind the need to get a souvenir. You want to, somehow, take a part of what you lived home with you. More than just memories, it is like a need to take a physical part. For some people, pictures and movies serve that purpose very well.
It is a very personal decision how you raise your children and none of my business to intervene, but I agree that it can be frustrating and a waste of money when things end up in the trash. However, you may be able to turn it around so they do not end up in the trash faster than any other items! For example, you could get them something practical such as a good piece of clothing that won't wear out easily, the child's personal mug, a pencil for school, etc.
What I do trying to prevent the waste you make reference to is, rather than letting them buy any action figure they see in the parks (which do end up rolling all over the floor when the novelty wears out anyway), I advice them to buy something they'll use in school. It seems to help.
Just my respectful, personal $0.02...