12 is what we already have. So nothing would have to change in that regard. We could keep the names as they are, despite the fact they are out of order as it is.
I used to think the same way, but after seeing this calendar, it would be easier to integrate this into what we currently have, just the amount of days have changed.
And, this calendar would work well with businesses. Most businesses are based on quarters. Not that it is significantly more difficult to track 13 weeks (they would be static after all), the pushback would be less, arguably.
And the world calendar is cyclical, just on a quarterly scale, rather than a monthly scale. I'd argue the monthly cycle makes more sense. But the math of the Earth's rotation doesn't make for a nice calendar.
I feel the world calendar would be easier to integrate, and a little nicer (I am a huge advocate for base 12 anyway, that's always been a big hangup for me for the international fixed calendar).
It's also so obvious. Not sure how I missed it. I'm stealing the idea. It shall be named whiddershins' calendar.
This would make the days of the week always cycle synchronously with the days of the month.
Then you have one day left over for New Years and that extra Leap Day every 4 years that your linked calendar proposes.
If you are going to redo something like a calendar, ending up still having different length months and weeks that drift against them seems like a non-victory.