Cardboard, paper, etc. seems like the perfect tool...trash becomes handy. However, the issues with paper/cardboard items and chemicals are real and complicated. This link should be enough of a starting point to go down the rabbit hole:
https://www.paperonweb.com/che...
So it isn't simply glues and definitely not just wood pulp.
The FDA in the US addressed just 3 chemicals in wide use for things like pizza boxes. That only scratches the surface. Look on the bottom of a LOT of produce boxes. Many contain warnings regarding reuse.
We all make our own decisions of acceptability but I've put in far too much effort and time to build long-term resources here to not consider the precautionary principle. I don't use paper in the compost. Usually what does come onto property as a result of shipping and/or transport leaves just as quickly. Almost anything could be used for something else or in new ways. I guess I'm trying to say that I try not to let "can be doing" override "should be doing".
I'm already dealing with decades of coal burning and don't feel like I need to be trading current legacy issues for future potential ones. YMMV.