This turns out not to be the case.
IPv6 will not reduce the size of the routing tables. Anybody with prefixes, and PIAS right now, will likewise get a /48 of IPv6 space and start advertising it into BGP.
If anything the more easily available space may result in bigger routing tables as a result. (Not everyone was able to get a /20 - particularly outside of ARIN space. For example - IPv4 addresses come very dear in places like Dubai.)
And NAT doesn't go away with IPv6. That was another belief that did not survive its first encounter with reality. It's simply called "Network Prefix Translation" now (NAT by another name)