I don’t see anything wrong with that. The dog is not giving away anything valuable, and if this makes them both happy, that should be fine.
Just take a video, if possible and share it.
Actually, properly packaged and disposed of trash has a high value—its labor value. That’s the value of the time and effort it took to collect it and pack it for disposal. If it’s ripped up and spread all over everywhere, the Labor Value of that trash massively escalates since it must be recovered and repackaged.