As homo sapiens aren't the only dumpster divers, maybe instead of looking for the government to give you a sense of security over your discarded goodies, we would all be the wiser by looking to nature and how some communities have then dealt with the "problem".
Enter the Bear Box, built to government spec to keep dumpster diving bears at bay--modifying a few of this product's features to keep the human animal at bay might be a wiser move than outlawing trash scavenging, curb crawling, bin trawling, and other forms of refuse reallocation.
Those who feel threatened by the dumpster diving hobbyist and the economically marginalized can then meander on over to Walmart and pick-up their Dumpster Dive proof trash bin. That is the perfect future, but, in the mean time, the truly concerned individuals can at least head out to their nearest big box store--take some personal responsibility--and buy, as well as use, a paper shredder on their potentially compromising documents.
Laws or not, that is the wise action to follow--especially when there are potentially identity thieving bears on the loose, as this clip demostrates: Dumpster Diving Polar Bears Caught in the Act.