If I knew your computer's address (and it didn't change) and you knew mine, we could route traffic through the infrastructure we already pay for.
It will at least address the NAT problem. Theoretically, if ISPs truly embrace it, it will also open up the possibility of direct P2P communication across most devices on the Internet. Can't remember if there's a standardized protocol for IPv6 like UPnP but if not you can just configure your firewall manually. Of course, that's assuming ISPs allow you to do so.
Tbh, I misread your OP and I somehow got the idea you were talking about NAT. Static addressing is also a problem but a smaller one. In fact, IPv6 probably does nothing to help here, and may even make the problem worse with address randomization (which is a legitimate privacy feature, but still).