A default deny firewall is a good idea to protect services everywhere in your network, including those which run on the router itself (e.g. many routers run a local DNS server.) Without NAT, packets are not dropped, they simply do not have their destination rewritten to another device on the network. The traffic is still destined for the router and will be processed by it. This is why routers ship with a default-deny firewall rule.
NAT is not a firewall. It is address translation. It will not drop packets.
Sure, a default deny is a good idea. However, it's not _critical_. If you forget to enforce it on your NAT router, you'll be fine. And if you are behind a CGNAT, it's even safer.
In IPv6 it becomes absolutely essential. If you forget to include it, your network becomes wide open. And you don't have an easy way to detect this because you need an external service to probe your network.
> NAT is not a firewall. It is address translation. It will not drop packets.
Yes, it is a firewall because it enables the address space isolation.