It's not very hard to send packets with a fake source IP, especially if you don't care about the reply.
That also means that every router now has to maintain a connection table to keep track of all of the pending confirmations, and to periodically check that table for expirations so it can clean it up. Maybe not that bad for a local router, but this is completely unworkable for routers handling larger parts of the internet.
And of course, anyone who has a tap into that level can trivially spoof all of the correct replies so it's still not a secure mechanism.