In parshas chukas (20:8), right before Hashem tells Moshe to speak to the rock, Hashem instructs him to take his staff. Why instruct Moshe to take the staff, if he was supposed to speak to the rock and not hit it?
According to the Chizkuni,
“take the staff!” G-d referred to Aaron’s staff. This is clear from what the Torah writes: Moses took the staff that had been in the presence of the Lord, i.e. in the Tabernacle, the staff that had produced almonds in Numbers 17,23. Compare also Numbers 17,25, where Moses had been told to return his staff to the Tabernacle as an ongoing reminder to the obstinate community of Israel that a member of his family had been chosen to be High Priest. It was appropriate for this staff to be used again when dealing with a people that were in a rebellious mood. In this episode Moses committed his first error when he took the wrong staff, seeing that he thought he was supposed to strike the rock. The only reason that G-d had told Moses to take this staff, was that it had been used in conjunction with the rebelliousness of the Jewish people, as opposed to the obstinacy of Pharaoh.
Whereas the Sforno writes
G’d commanded that as soon as the rock would yield up its water, Moses was to use his staff in order to guide separate streams of that water to the various areas in which each tribe had its tents, so that they would not have to leave their homes, as they did to collect the manna, in order to benefit from this vital resource.
Targum "Yonasan" says that Hashem told Moshe to take the staff as a backup option. In case speaking to it didn't work, he would then hit it so it would release water. Which is an interesting explanation, as why wouldn't the rock listen? Perhaps the people wouldn't be worthy? Hashem knew...yet He wanted Moshe to do the proper diligence? Anyways, here's the text:
סַב יַת חוֹטֶר נִיסַיָא וּכְנַשׁ יַת כְּנִישְׁתָּא אַנְתְּ וְאַהֲרן אָחוּךְ וְתוּמוּן תְּרֵיכוֹן יַת כֵּיפָא בִּשְׁמָא רַבָּא וּמְפַרְשָׁא כַּד הִינוּן חַמְיָין וְיִתֵּן מוֹהִי וְאִין יְסָרֵב לְאַפּוֹקֵי מָחֵי אַנְתְּ לְחוֹדָךְ בֵּיהּ בְּחוּטְרָא דְבִידָךְ וּתְהַנְפֵּק לְהוֹן מַיָא מִן כֵּיפָא וְתַשְׁקֵי יַת כְּנִישְׁתָּא וְיַת בְּעִירֵיהוֹן
Take the rod of the miracles, and gather the congregation, thou, and Aharon thy brother, and both of you adjure the rock, by the Great and manifested Name, while they look on, and it shall give forth its waters: but if it refuse to bring forth, smite thou it once with the rod that is in thy hand, and thou wilt bring out water for them from the rock, that the congregation and their cattle may drink.
Not an answer really, more expanding the question: End of Parshas Beshalach, Exodus 17:9, Moshe does a similar thing. Yehoshua is sent to fight Amalek. Moshe says that "I will go to the top of Giv'ah - with the staff of G-d in my hand." But then the narrative continues, "When Moshe would raise his hand(s), Israel would win, when he would lower his hand(s), Amalek would win..." Our sages in Rosh Hashana 29a comment, "Is it conceivable that the hands of Moshe could make war or lose a war? But it is to tell you, whenever Israel would look on high, and subjugate their hearts to their father in heaven, they would win..." I might have thought that the hands of Moshe - holding that staff - could indeed help to win a battle!
I haven't seen a description of what Moshe did with the staff [pictures of the battle never seem to show it, and indeed people never remember it, being mentioned a couple of verses too early]. But I didn't see either that he did anything with the staff at Makas Bechoros, slaying of the first-born ('לא ע"י מלאך כו) - and yet our sages say that all ten plagues were inscribed in the staff: דצ"ך עד"ש באח"ב. It was created Erev Shabbos along with all the miraculous objects (Pirkei Avos 5(6)), and I guess the staff represents all the occasions where Hashem overruled the laws of nature to help his people.