Yes, from a seasonal perspective, the timing of a season varies idiosyncratically from place to place. That was the first thing I said. Why would you then want to locate the beginning of Fall on the equinox?
Quoting from your link:
> seasonal lag is not "seasonally symmetric"; that is, the period between the winter solstice and thermal midwinter (coldest time) is not the same as between the summer solstice and thermal midsummer (hottest time).
> In mid-latitude continental climates, [seasonal lag] is approximately 20–25 days in winter and 25–35 days in summer.
> there is no meteorological reason for designating these dates as the first days of their respective seasons.
Not only did I not ask that, I don't believe that the equinox is traditionally known as the beginning of autumn. Traditional terminology always marks the solstices and equinoxes as the middle of the season in which they occur, because that is obviously the way seasons work. Compare Western European "Midsummer" [the solstice] or Chinese 立秋 ["beginning of Fall", August 8; compare to the equinox on September 23, or to the "Mid-Autumn Festival" 中秋节, fixed to the full moon, but generally around late September].
The equinoxes and the solstices are marked on modern calendars as the beginning of their respective seasons, but I have never heard anyone attempt to justify that. I tend to assume it's the result of the calendar-buying population not having any reason to care what season it currently is.
But even among modern calendar-buying people, I believe they think of big snowdrifts as something that happens in winter, not something that happens in late fall and continues through winter. And the calendar doesn't agree with that.
Quoting from your link:
> seasonal lag is not "seasonally symmetric"; that is, the period between the winter solstice and thermal midwinter (coldest time) is not the same as between the summer solstice and thermal midsummer (hottest time).
> In mid-latitude continental climates, [seasonal lag] is approximately 20–25 days in winter and 25–35 days in summer.
> there is no meteorological reason for designating these dates as the first days of their respective seasons.