IPv4+NAT does not remove any more classes of problems than IPv6+firewall. Firewalls under IPv6 work exactly the same way as they do with IPv4.
An IP connection is started from the 'inside' to the 'outside', and the source-destination tuple is recorded. When an 'outside' packet arrives the firewall checks its parameters to see if it corresponds with an existing connection, and if it does it passes it through. If the parameters do not correspond with anything in the firewall's table/s it assumes that someone is trying to create a new connection, which is generally not allowed by default, and therefore drops it.
The main difference is that with IPv4 and NAT the original (RFC 1918?) source address and port are changed to something corresponding to the 'outside' interface of the firewall.
With IPv6 address/port, rewriting is not done. Only state tables are updated and checked.
New connections are not allowed past the firewall towards the inside with either protocol, and only replies to connections opened from the inside are passed through.
There's no magical security behind NAT: tuples and packet flags are read, looked up in a state table, allowed or not depending on either firewall rule or state presence.
The security comes from the state checking.
> […] and it was happily listening on the public internet for something to print.
I have a printer with an IPv6 stack. I also have IPv6 addresses from my ISP. Yet somehow my Asus AC-68U prevents the public Internet from reaching my printer…