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>same algorithm for determining which years are leap years as the Gregorian calendar

It's ridiculous to propose overhauling the calendar without addressing what is IMO one of the most annoying parts about dealing with calendar dates.

And what alternative do you have in mind? We could redefine how long a year is. But that would require some tricky orbital engineering and a very large rocket.
I don't have a serious suggestion. It would indeed necessarily involve decoupling the calendar year from the seasonal year. Three 487-day "years" lines up with 4x365 + 1 leap day, and the seasons are still regular (over a longer period).