We know you feel the extra in the ordinary when you open a particularly well made cardboard package :) You may be a grown adult, but how many times have you thought "hmm that's a nifty little box!'. You care already.
Because once you notice the extra, everyone will
Remember when no one cared about plastic? And to be honest, microplastics aren't even considered a major threat by environmentalists. The more conscious you are of packaging – eg. the more you know that cardboard packaging is second only to "none", the more corporations and businesses will care.
Because you can judge a product by its box
Choosing a good box is a sign of attention to detail you want from the maker of your fill-in-the-blank. It shows respect to the thing-itself, to you and to the environment. You should care, because they should care.