Almost all of this would be true if we celebrated a day (or two) each year that were outside of the months and weeks, except events tied to points in our orbit would stay put a lot more. We would still have the same calendar every year. In your version we have a full extra week every 6 or so years, in mine every year we have a dedicated New Year's Day that isn't in a regular month or a day of the week, and every 4 or so years (same rules as now) we have 2 New Year's Days.

Though I would argue for Sunday being the 1st day of each month/year. IMO weekends should be like bookends, one on either side.

Edit: your Wiki link contained a link to the International Fixed Calendar, which I've been inadvertently arguing for. This is almost identical to what I've been proposing, except they put the leap day at the end of June. But it fixes the major disadvantage of your system: that a year isn't a year. In your system 1/1 is never one year away from 1/1. In mine it is within leap day drift, just like the current calendar.