Martian packets are a funny thing: The packet is ALWAYS coming from somewhere, so why don't internet providers just flat out refuse to send packets exiting thei

Martian packets are a funny thing: The packet is ALWAYS coming from somewhere, so why don't internet providers just flat out refuse to send packets exiting their networks if the given IP doesn't match what they get? Okay, routers are supposed to get a packet and just route it to the next point by blindly following the instructions ("0.0.0.1 wants to UDP 124.40.28.9 on port 80"), but whatever the route taken, once my route leaves my home router, my first stop will ALWAYS be my provider's routers, the very company that gives me an IP. So why can't these companies check on their client-to-outside-world routers that the request is coming from my IP and not something otherworldly?