Is there a legitimate reason why any ISP / hosting provider etc allows traffic to exit with an IP that doesn't belong to them?

Surely enforcing this would prevent any IP spoofing, which would cut down on these types of attacks?

(As far as I'm aware in this type of attack you send packets purporting to be from your target, to anything on the internet that will blindly send back a reply. Hopefully the reply will be bigger/more packets than your request was, thus amplifying the bandwidth).

If I'm mistaken please explain why...