Even with private networks, having plenty of address bits makes things a lot easier. My employer's internal network includes hosts with addresses in the 10.0.0

Even with private networks, having plenty of address bits makes things a lot easier. My employer's internal network includes hosts with addresses in the 10.0.0.0/8 private address range. So does my home network. I have to be careful when choosing subnets, or else things will break in weird ways when I connect to my work VPN. With IPv6, I don't have to worry about this because every machine can be assumed to have a globally-unique address, even if that address isn't normally exposed to the outside world. And more importantly, it's easy to look at the address prefix and figure out where to route packets.