It doesn’t affect us day-to-day no, but honestly I like being part of a ‘Commonwealth’. I like feeling like I have something in common with Australia, or New Zealand, or the UK, even if I’ve only ever been to the UK for a few hours.
Your family name (for most people, unless you’re George Hitler) has no impact on your day-to-day, this to me seems like saying “We should just get rid of family names!”
The people who are being manipulated with this nationalist dog whistle see no value in being a member of the Commonwealth. Canada First and MCGA and all.