Perfect people don't poop. The perfect digestion system would utilize everything eaten by the perfect mouth. The Bible says that Jesus ate and drank, but it never says he pooped or peed... because he NEVER did. Even when Jesus was a kid and his parents couldn't find him, every other parent would look for their normal kid in the bathroom, but Mary and Joseph knew that was someplace Jesus wouldn't ever need to be.
Animals have always pooped and always grown old and died. God made them that way. But he made perfect people to never poop and never grow old and die.
Was this perhaps an additional issue that God added on when Adam and Eve
sinned (such as Eve having significant more birth pains)?
It's the "stain of sin." Just like god made the rainbow to remind us about the flood, he made underwear skid marks to remind us about the naked lady eating the apple she got from the talking snake.
Of course there are probably some revilers here who will say, "If we were never supposed to poop, then why do we have buttholes, Billy?" Duh, perfect people have magical farts. Jesus' farts could make the blind see, the lame leap, the dead rise, and lure fish into the nets. Just imagine after armageddon when all the survivors can focus their farts into making a global paradise!