@voxofgod the Commonwealth doesn't want the USA, that's not going to happen. Also, I'm kinda of getting the impression you think it's a bit like the EU? Commonwealth is basically just the old British colonies kinda maintaining some cultural (and sometimes head of state) ties after independence. In practice it just means some countries like Canada and Australia still have the UK monarch as a powerless head of state. We don't get freedom of movement like the EU gets. I don't think we even get special visa conditions.
In practical terms, being a member of the Commonwealth means your country gets to take part in the Commonwealth games. And maybe extra diplomatic help in other Commonwealth countries if you don't have an embassy there. Um. That's it afaik 
Btw New Zealand is not disability friendly for immigration. There was a big story a few years ago where a British man was offered a high paying job there and was told he can take his wife and older child, but his disabled daughter was not given residency.
When trying to find the article, I found these:
https://news.sky.com/story/girl-12-denied-residency-because-her-autism-does-not-meet-acceptable-standards-of-health-in-new-zealand-12599259
https://metro.co.uk/2019/03/26/family-denied-visa-daughter-downs-syndrome-9022812/
https://www.liveaction.org/news/new-zealand-denied-residency-teenage-girl-syndrome/