> If every IPv4 address were a valid IPv6 address, then these statements wouldn't be true.
This is already the case. The format for representing IPv4 addresses in IPv6 is to encode the first 96 bits of the address as ::ffff and the last 32 bits as the IPv4 address, e.g. 192.0.2.128 as ::ffff:192.0.2.128. You can also encode the last 32 bits as hex if you want (::ffff:c000:0280 is the same address) but then it's less obvious what the IPv4 address is.
The problem is that every IPv6 address is not a valid IPv4 address, because the IPv4 address space is smaller so there is no way to do that without some kind of NAT or similar, which also exists but sucks in various ways.
