I don't see any CANZUK bloc at all because the geographical location of the members is not contiguous or anywhere near contiguous. The two countries that are geographically closest together are Australia and NZ with about 1,600km between them. Canada and the UK have the Atlantic Ocean between them. Australia and NZ are in the low to mid southern latitudes in the eastern most longitudinal quadrant of the eastern hemisphere. Meanwhile Canada and the UK are in the mid to high northern latitudes in the western hemisphere. Politically I see do not any political will for it from any of the national governments.
Economically all four nations are in the CPTTP but of the four nations, Canada has the most protectionist economic policies. In fact NZ has taken Canada to the WTO because of its highly protectionist policies. However I have seen some suggestions that the CPTTP members either invite the EU into the Treaty or work closely with the EU to mitigate Trumpian tariff policies and actions. There is some merit in such a suggestion. The other thing that the CPTTP has to consider is whether to approve the PRC application. Thinking at the moment appears to be that the PRC doesn't meet, nor will be able to meet the CPTTP requirements for transparency, accountability, and ethics in trade practices, legislation, and jurisprudence. Personally I think that it is not in the best interests of the current CPTTP membership, politically and economically, to admit the PRC.
On the free movement of citizens between the four countries, they are not going to agree to it. All of the four nations have restrictive immigration policies with both Canada and NZ have some of the strictest immigration policies in the world. Australia and the UK aren't far behind.
Militarily there is little to offer because of the geographical disparities. The UK has visions of military greatness but its forces are run-down and under resourced. It cannot afford to do much more and some claim that it's in danger of being classified as a third world economy, second world at best. It's politicians have champagne dreams of granduer on a lemonade income. A classic example is their current two QE CVs. They are a pure egotistical project that has illustrated a lot of what is wrong with UK defence since 1991.
Canadian military procurement is one of the most problematic in the world, second only to India for inefficiency, bureaucratic mayhem, and political stupidity. Canada has good forces but like the UK they have been handicapped by the politicians and government bureaucracy. NZ is another country where the politicians and government bureaucracy has severely constrained the defence force because of ineptitude and political daydreaming, plus having champagne dreams of granduer on a lemonade income. Of the four CANZUK nations Australia is the only one that has adequately resourced and equipped its military even though it isn't immune from self inflicted stuff ups.
From a southern hemisphere POV, it would be better if Australia and NZ formed closer defence relationships with South Korea and Japan, plus India if possible. From a NZ POV, significant treasure and resources will have to be expended upon defence, plus significant effort put into such closer relations by the NZ political and bureaucratic elites. They will have to back their words up with actions.
