Actually, after considering this I think that Setsubun no hi coinciding with 2.2.2 or 2.2.22 will be vanishingly rare in both Western and Japanese calendars, because setsubun no hi usually falls on February 3rd. This year's February 2nd setsubun is a "once in four years" kind of exception to keep the date aligned with the start of spring as determined by the orbit of the earth around the sun. The calendar gets whacked into alignment with the seasons by means of a leap day every four years (with additional fine adjustments that we don't need to get into here).

In 2022, setsubun no hi will fall on Thursday, February 3rd.
Last year's setsubun no hi was Reiwa 2.2.3 and it was not a palindrome.

From next year, setsubun no hi will fall on February 3rd except in years that follow leap years, when it will fall on February 2nd:
https://dengekionline.com/articles/61893/

I can't get my head around how it is that setsubun no hi can fall on February 4th, but it sometimes does - In 1984, the vernal equinox first day of spring fell on February 5th and shunbun no hi was the preceding February 4th.