I think they are referring the the shear number of IPs available and ease of switching.

Not a solid argument, but it is the only thing I can think of though for their argument.

Yes, but "network" itself is an abstract concept. Because the addresses aren't scarce you can theoretically get a new one every day, or every time you log on, and throw it away right after. Each device you own can also have its own IP, without any NATs in the way and no way to tie them together.

IPv6 has the advantage that the ISP can give customers multiple prefixes at the same time, thus allowing rotation of the prefix without interrupting existing TCP connections.

With IPv4, ISPs that want to rotate IP addresses have to forcibly disconnect their users (e.g. every 24h). This is a common practice, though probably mostly intended to allow charging business customers more if they need a stable IP. But the privacy side effect is also nice.

But other than that minor point (which many ISPs are not taking advantage of), IPv4 addresses and IPv6 network prefixes are essentially the same privacy-wise: uniquely identifying an ISP customer, i.e. a family, not an individual.