People quickly realized this flaw, and updated the standard so that basically your client gets to pick the second 1/2 of your address now. And the nice thing is, most major platforms will actually run multiple addresses in parallel, allowing new connections to use a new address while old connections keep using the old one.
So while ipv4 adds some protection by having multiple clients behind the firewall, ipv6 actually makes it better by looking like even more clients behind the firewall.
Combined with a browser that blocks fingerprinting you get slightly better privacy with ipv6.