Re: What has it got in its pocketses?
Do you mean a regular home CPE? That would be difficult, as very few of them don't support NAT.
This really should be obvious, but... the fact that NAT support is common in home CPEs does not mean that NAT is free to implement, or that the implementations never have bugs, or that it doesn't introduce additional complexity into networks or software, or that it can't cause problems. To be clear: it costs money to implement, the implementations have bugs, it makes networks more complicated, it adds complexity to software and it causes lots of problems. All of these issues are part of the cost, which you pay for either with money or with time, effort and frustration.
At the ISP side, NAT is done on routers that cost in the £10k-100k range. NAT may be an additional license cost, and it also imposes a performance hit that means you need to buy more of the expensive routers than you do without it. Since internet traffic is increasing over time, the additional costs of NATing that traffic also increase over time. Dual-stack ISPs see over half of their traffic flow over v6, which immediately reduces the cost of the routing hardware needed to NAT the remaining v4 traffic.
Depending on the ISP network, CGNATed traffic may need to be routed out of its way in order to reach one of their CGNAT routers whereas v6 traffic can be handed off early, which increases the latency of v4 traffic. This too is a cost you pay.
So, yes. The cost of NAT.
As for why v4 addresses are in demand, it's a combination of the cost of the workarounds required when you don't have enough address space (including but not limited to the stuff I just wrote three paragraphs about), and the fact that there are a large number of v4-only clients out there that you still want to provide service to. To be clear again: these are reasons to be doing v6, since the address shortage in v4 isn't going away.