This page lists 4 rules that may cause the first day of Rosh Hashannah to be postponed from being on the date of the molad Tishrei. One of the rules is:
If molad Tishri occurs on Sunday, Wednesday, or Friday, Tishri 1 must be delayed by one day for the following reasons:
Wednesday or Friday would cause Yom Kippor (Tishri 10) to fall on Friday or Sunday making it impossible to prepare food (because of Sabbath restrictions) on either the day before or the day after the Yom Kippor fast. Sunday would cause the seventh day of Succoth (Hoshana Rabba) to fall on the Sabbath.
OK, I understand that on Hoshannah Rabbah, there is a custom to beat the aravot twigs on the ground, and we cannot do this on Shabbat.
I'm curious as to why the calendar rules would be that concerned about performing what is a minhag rather than giving priority to performing a Torah commandment such as assuring that Rosh Hashannah never falls on Shabbat so that we can always be sure to blow the shofar on Rosh Hashannah?
I know that there are 2 days of Rosh Hashannah, so if we miss blowing on Shabbat, at least we know that we will hear SHofar blowing on Sunday. OTOH, Hoshanna rabbah is 1 day so if we don't beat the twigs that day, there's no other day to do it.
Nonetheless, shofar is still a Torah commandment, and the Torah says that there is just 1 day of Rosh Hashanna. The fact that we have 2 days is b/c we are following the sfeika deyoma rules. But it is still a Torah law vs. a minhag. I would think that performing the Torah law would be more important and should have precedence in deciding these postponement rules.
My Jewish history timeline is bad. Which came first? The establishment of the calendar via Hillel IV, which we now use, or the minhag of beating the aravot on Hoshannah Rabbah. I don't think this is mentioned in the Mishnah or Gemarrah, but I may be wrong.