Our Gemara on amud beis describes the practice of beating the aravos on Hoshana Rabbah as a custom stemming from the times of the prophets.
What is a custom of the prophets ? They had the power to make takkanos decrees obligating observance, so why decide to make something a custom? It seems to occupy a place that is not a mitzvah, even rabbinically, and this is why no blessing is recited. However, the deeper question is if it is worthwhile why not legislate it, and if it is not worthwhile, why bother? The simple answer is that it must not be as imperative as a regular mitzvah, but this explanation does not sit so well. Why does this custom rate less than lighting Chanukah lights? In fact, certainly history judges the custom of beating the arava branches on Hoshanah Rabbah as significant. We still do it to this day!
The simple answer is that other types of rabbinic ordinances were one of two functions: (1) to commemorate some historical development such as lighting of Hanukkah candles or reading the Megillah, or (2) as a kind of preventive measure such as the laws of Muktzah or Yichud. However, this is a new ritual that was not described by the Torah. Even though we have the rabbinic institutions of prayers and blessings, they are based on an overall biblical ethos and commandment to pray. However, this is a specific action ritual. Perhaps the prophets considered it to be impetuous, and even a violation of Bal Tosif (do not add to the Torah) to institute it as a formal ordinance.
There are deeper mystical explanations to supplement this as well. The Ishbitzer (Tiferes Yosef Hoshanah Rabbah) explains that The function of mitzvos in general is to integrate the material world through action into the spiritual world. This is really the meaning of the phrase in the blessings, “Who has made us holy through His mitzvos“. However, there are actions that are so spiritual and so non-rational that they go beyond even the conversion of physical matter into spiritual. They are simply mindless (but not empty, God forbid) acts of devotion. This is represented in this custom of the beating Of the Willow branch. The Willow has no odor nor taste; it is devoid of everything. And by performing an almost mindless act with our body and our hearts we hope to breathe life into the ultimate emptiness, even emptiness that cannot even be filled by the regular commandments.
I will try to explain this a bit more. Tertullian exclaimed, “Credo quia absurdum”, "I believe because it is absurd". What he meant is that God is so unknowable that the attempt to understand is ridiculous. The only thing to know is that everything is empty without God, and so the only thing that makes sense is to believe, even though we don’t even really understand. The world is impossible, but it exists, so we must accept the impossible as the only possible. As long as I am name dropping philosophers and theologians, it is what Kant describes as the impossibility of a priori knowledge of metaphysical reality.
I think the Ishbitzer is saying through this custom there is total surrender of meaning and logic as a way to reach God through non-rational means.
Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation 
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