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The vernal equinox is not just a day; it is a specific moment in time. It is the moment where the sun appears to cross the “celestial equator” from south to north. The Persian calendar does not begin at the specific moment of the vernal equinox. The Persian calendar year starts at the midnight in Iran that is closest to the equinox, which can deviate by plus or minus 12 hours year to year. Some years will begin up to 12 hours before the equinox; some years will begin up to 12 hours after the equinox.

That deviation greatly exceeds the differences described in your link. All tropical solar calendars have this same issue. You’re talking about the seconds and minutes that these solar calendars slip over thousands of years, but you’re ignoring the many hours that they vary from year to year.

While the Persian calendar may be incrementally superior to the Gregorian, if we are looking for one that actually achieves the objectives you describe, we should go ahead and adopt the Sidereal Calendar, which is currently used by astronomers who need the degree of accuracy that it provides. The sidereal calendar is arbitrarily accurate. It as accurate as we care to measure, both year by year and in perpetuity.