Anakin doesn't just pick up the ones Obi-Wan discards on the battlefield, sometimes he just straight up steals them out of Obi-Wan's closet. And probably he steals some of Obi-Wan's blankets every so often, as soon as the ones he has lose their smell, he goes to replace them, because, look, there are a lot of things I'm willing to bend on, but Anakin Skywalker having an Obi-Wan shrine in his closet with a nest and probably some fairy lights strung up as well, IS NOT ONE OF THEM. ;)