It is a hard and fast rule that we do not rely on miracles ('Ein somchin al ha'nes'). Generally speaking, we are expected to do something towards our own salvation, just like we are expected to do something towards earning a Parnasah.
We do realize of course, that we do so only because G-d wants us to, and that in reality, it is He who finishes the job, and it is by His grace that our efforts succeed. It is not because G-d needs us that He asks us to put in our own efforts, but as the Ramban explains in Parshas No'ach, it is to minimize the miracle and to increase the aspect of nisoyon (trial). This is linked to Emunah and Bitachon, which in turn, are vital to our Avodas Hashem. In other words, witnessing open miracles interferes with our free-will and choice, and will result in less reward for the good deeds that we perform.
To be sure, there are occasions, rare occasions, when G-d performs open miracles without our participation, but to ask us to refrain from participating, even when we are ready to, goes against the principle of 'Ein somchin al ha’nes'.
This being the case, it does indeed seem strange that at the Yam-Suf, *G-d instructed Yisrael, "Hashem will fight for you, and you shall be silent", implying that, from that moment onwards they were to desist from both prayer and positive participation in the battle that was about to take place.
The Or ha'Chayim cites a Yalkut Shim'oni in Shmuel, which refers to four kings who made demands of Hashem (in time of war); David said to Hashem "Let me pursue my enemies and overtake (and kill) them". Asa declared that he was prepared to pursue his enemies, but requested from Hashem that, since he did not have the strength to destroy them, He should destroy them on his behalf. Came Yehoshafat, and claimed that he did not even have the strength to pursue his enemies, so he suggested that Hashem save Yisrael whilst he sang Shirah.
And finally, there was Chizkiyahu ha'Melech. who declared that he did not even possess the strength to sing Shirah, so he prayed for Hashem to destroy the mighty army of Sancheriv whilst he slept. In each case, Hashem responded favorably to all four requests - He allowed David to defeat his enemies, Asa chased and Hashem destroyed, He vanquished the enemy whilst Yehashafat recited Tehilim, and He destroyed the camp of Ashur whilst Chizkiyahu slept.
K'lal Yisrael, the Or ha'Chayim concludes, were on the level of Chizkiyahu ha'Melech. They were overcome by a feeling of inadequacy in their helplessness, not in a position to vanquish, not in a position to chase, and unable to pray. So G-d took over completely.
But this is difficult to comprehend. For with Chizkiyahu, it was he who expressed the feeling of utter helplessness, coupled with a total faith in G-d's ability to initiate the salvation without him. Whereas here, the command to desist was issued by G-d, as we pointed out.
Rabeinu Bachye explains that Paroh had just recently experienced the ten plagues, culminating in Makas Bechoros, and had finally agreed to let G-d's people go. Chasing after K'lal Yisrael in order to return them to Egypt was an act of extreme defiance against G-d. In short, it was not Yisrael who was Paroh's intended victim, but G-d himself (ke'vayachol). And that, he concludes, is why G-d considered this to be His personal battle, and explains why He ordered Yisrael to refrain from participating.
It is also possible to resolve the current problem in light of what we explained last week. We wrote there that K'riy'as Yam-Suf was the punishment that G-d had long reserved for Paroh for his maltreatment of K'lal Yisrael (measure for measure for the latter's drowning of the Egyptians, as Rashi explains in Yisro). Indeed, this was what He had in mind when he told Avraham Avinu that He would punish the nation that would subjugate them (as we explained).
Generally speaking, when K'lal Yisrael is attacked, it is in the form of a punishment. Take for example, the episode of Amalek, one that occurred in this very Parshah. Amalek attacked them suddenly, as Chazal have explained, because their Emunah was weak (see Parshah Pearls, 'Erasing Amalek'). He was, so to speak, the stick that G-d brandished to admonish Yisrael. And that is when K'lal Yisrael's participation was vital in the form of prayer and the mobilization of troops to go to war.
K'riy'as Yam-Suf however, was different. The purpose of the chase was not to punish Yisrael, but to lure the Egyptians down to the Yam-Suf, in order to punish them. And this explains why Yisrael were ordered to 'borrow' the Egyptians' vessels when they left Egypt, why G-d created the impression that Yisrael were lost in the desert, and why He made them camp in front of Ba'al Tz'fon, which, alone from all the idols of Egypt, had been left standing after Makas Bechoros for that very purpose. Indeed, that was why G-d took them via that roundabout route to begin with.
It transpires, that the Egyptians were not the stick; Yisrael was the carrot! Yisrael were not in the least threatened by the Egyptians, and any impression that they were was no more than an illusion. G-d was settling an old score with the Egyptians, and the strategy that He chose to employ, involved the extensive, but passive participation of K'lal Yisrael. True, Yisrael, who were unaware of all this, suffered a most terrifying ordeal, but they were well compensated by, not only witnessing, but actually being part of, the most incredible miracle that ever took place in the history of the world. And not only that, but they then merited to see their erstwhile enemies dying in front of their eyes, not departing the scene before walking off with a vast haul of booty that even exceeded the huge amount of Egyptian treasures that they took out of Egypt - without having as much as drawn a sword from its sheath.
*Like in the first Geula, may it be IY”H in the final Geula.