Why Can't Moshe's Hands Perform Miracles?

Question

The Torah (Shemos 17) describes a battle between Israel and Amalek in Refidim, and says that when Moshe's hands were raised, the Israel would be winning, but when he lowered his hands Amalek would overpower them. On this story, Chazal (Rosh Hashana 29a) ask, "do Moshe's hands wage war", and explain that his hand raising was merely a way to direct the nations' minds towards heaven.

Why can't the explanation simply be that Moshe's hands were a means for God's performance of miracles? After all, before this story, Aharon hit a river and it turned to blood or spit out swarms of frogs, Moshe hit the sky and various miracles occurred, he stretched out his hand/staff over the sea and it split, and he had most recently (Shemos 16) hit a rock and a spring of drinking water burst out of it. Clearly, God wanted miracles to be performed via Moshe's hands (or staff); why don't Chazal ask "does Moshe's staff split seas?"

Answer 1

A simple answer would be that the effort to support Moshe's arms implies that his arms themselves were winning the war. If it was just an arbitrary medium through which Hashem would perform a miracle, the why go to all the hassle f holding up the arms-just switch media. Therefore, in this case in particular Chazal emphasize that the victory actually depended solely on Hashem.

The Netziv asks the question in Meromei Sadeh to Rosh Hashanah here. He answers (if I understand correctly) that the battle against Amalek had to be performed by natural means and therefore the Mishna couldnt say that his hands were simply a medium for divine intervention like other miracles performed through media. Therefore the Mishna says that it was to affect the Jews in the battle.
The Sfas Emes Al HaTorah to parshas zachor addresses the question also.