I'm not sure, personally. On an international level you're stronger if allied, but stronger isn't always good. The U.S. has been plenty strong, as there have been strategic gains moving alongside moral losses. When you can do a thing there's a temptation to actually do it, which is to your detriment when all sorts of bad things you previously couldn't do are now within your power. Not sure if this is an argument for smaller government or even smaller countries, but it's just an observation.
From the perspective of these commonwealth countries themselves, I think it's a mistake personally. All four of them have got significant authoritarian tendencies, maybe the UK in the lead here but I suppose it's close. All four countries have a tacit belief that anything the government does is ok; there is no pushback like there is in the U.S. against overreach, unconstitutional ideas, and loss of freedoms. The basic belief that government is your master is an inheritance from the British Empire, one which was never cast off as the Americans did. As a result, the stronger the government, the more entitled it is to create ways of life by fiat. And a 4-way alliance seems me likely to embolden them even further to start having policy fall in lockstep among them. This might well take the from of 'greatest common denominator', meaning the most extreme policy taken by one will be adopted by the others. I don't think anyone wants to see that, and in terms of the U.S., if there is already pressure for measures like lockdowns, there would be more pressure if the U.S. major partner "British alliance" is doing it.
