A bit incorrect. There are IPv6 protocol changes (ex. ICMP vs ICMPv6) where the newer protocols are more secure. But actually having a private IP behind a NAT gateway is more secure in general, because nobody can directly route to a host behind your NAT, without exploiting reverse NAT traversal. IPv6 will allow easier exploitation of default host configurations due to being able to route to them easier.
Will it? You'd still have to get around the router firewall, the host would have to have no firewall of its own and be exploitable and also you'd have to _find_ the host first.
This also needs to be balanced against the difficulty of exploiting servers that have been deliberately exposed to the internet, for example cameras or NASs. People often expose those deliberately (via port forwards on v4) so they can access them remotely.
v6 will make it harder to exploit those devices, because it makes it harder to find them in the first place. Most botnets that run on cameras etc spread via random network scanning, so making those devices harder to find makes it harder for botnets to spread. You can consider this akin to vaccination's effect on the R value for a contagious disease: vaccination can eliminate a disease even when it doesn't eliminate 100% of infections. If a botnet can't find enough vulnerable hosts to exploit, it'll die out.
NAT with port forwards makes it far easier to find devices like that, because it reduces the search space. v4 reduces the search space further still, to the point where it's quite feasible to do an exhaustive search.
On balance, I think this makes the larger address space (without NAT) less exploitable.
A bit incorrect. There are IPv6 protocol changes (ex. ICMP vs ICMPv6) where the newer protocols are more secure. But actually having a private IP behind a NAT gateway is more secure in general, because nobody can directly route to a host behind your NAT, without exploiting reverse NAT traversal. IPv6 will allow easier exploitation of default host configurations due to being able to route to them easier.