Is it common for routers to create a new mapping for TCP packets that is NOT SYN (in figure 3 in this article)? Is there a legit use case for this behavior? Wouldn't it be simpler and more secure not to do that?
Libp2p: https://docs.libp2p.io/concepts/nat/hole-punching/
B̶o̶t̶h̶ (update: Only Libp2p works with TCP) use similar method for hold-punching. Libp2p can use such method for establishing direct connection between hosts behind different NAT networks.
its meant to speed up connections and allow for more throughput through a router.
fast path changes the packet flow so it doesn't get processed by all firewall rules.
just explaining the use case for OPs question.