Just to share a different idea...
When my sons were young, they loved looking for shells and bringing them home, but we were conflicted about whether this was good for the environment, plus most of the shells they found were small and broken and smelly...
So one time, before a beach trip we bought some nice shells from a store and scattered them on the beach just before our kids got into that part of the beach (there weren't many other people in that area). They LOVED finding so many large and pretty shells, and we didn't feel bad about taking them with us because, after all, we had brought them with us.
Of course, it leads to another dilemma, do you let your kids forever think they hit the jackpot, or do you fess up and risk them feeling deceived? In our case, we fessed up later that day, once the initial excitement had died down. They were fine with it. They had kinda figured that something was up because they never usually find so many shells. Anyway, it was a nice memory for our family.
P.S. I don't think sand would be a problem in small quantities. After all, as a PP said, plenty comes home unintentionally in peoples shoes, etc., and no one is worried about that depleting the beach.