IP isn’t supposed to have “private address space”. The only reason it does is because the address space is scarce. NAT does not make your network “private” or provide security, firewalls and good host software do that. NAT literally breaks IP.
RFC 1918 describes space for entirely private networks, not “private extensions” to the public globally routable internet. There’s a subtle but important difference. The private addresses strictly aren’t routable on the public internet. NAT (which there’s also an RFC for) is what what allows packets to flow between private disjoint IP networks. IP is only scoped to work within a single network, whether it’s public or private or triangle.