The Frog

The Torah (Ex. 8:2) tells us how the plague of frogs began:

So Aaron stretched out his hand over the waters of Egypt, and the frogs came up and covered the land of Egypt.

The word "frogs" is actually in the singular in Hebrew, as if to say that a single frog came up. This led commentators to ask why it is in the singular, with some saying that it is merely a word that refers to a group of frogs. However, the Gemara (Sanhedrin 67b) relates two midrashic explanations of this grammatical anomaly:
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R. Akiva said: There was one frog which filled the whole of Egypt. R. Elazar ben Azariah said to him: Akiva, what do you have to do with Haggadah? Stop your words and devote yourself to Nega'im and Ohalos [i.e. Halakhah]. [Rather,] one frog croaked for the others, and they came.

According to R. Akiva, a single frog arose and then quickly multiplied into a swarm of frogs. According to R. Elazar ben Azariah, one frog arose and then called out for other frogs to join him. R. Elazar uses strong language to reject R. Akiva's view.

The Maharsha (ad loc.) explains that R. Akiva's explanation seems to contradict a later verse. After the next plague, that of lice, Pharaoh's magicians declare that it is not merely a trick but a miracle (Ex. 8:15), implying that the prior two verses were not open miracles but possible to duplicate through tricks. But if, as R. Akiva claims, the plague of frogs included the open miracle of a single frog instantaneously multiplying into thousands of frogs, then they should have declared that the plague of frogs was the "finger of God" and not waited until the plague of lice to say so.

Other commentators have different explanations of the difficulty of R. Akiva's view (e.g. R. Asher Weiss in his Minchas Asher suggests that R. Akiva's explanation undermines the midrashic lesson from the frogs jumping into the ovens [Pesachim 53b] - if the frogs were created specifically for this purpose then there can be no inference to normal creatures that were created to live). Be that as it may, it seems clear that R. Akiva's explanation is strongly rejected.

However, Rashi on the verse offers a single midrashic explanation and then suggests that "frog" refers to a group of frogs. Surprisingly, the midrashic explanation he offers is that of R. Akiva (link):

There was one frog and when they struck at it it would split apart into various teeming swarms.

Why does Rashi choose R. Akiva's rejected view over R. Elazar's? I haven't found a satisfactory answer to this question.

The Lubavitcher Rebbe (Likutei Sichos, vol. 16 p. 84) suggests that Rashi chooses R. Akiva's view over R. Elazar's because in the prior verse Aharon was commanded to raise the frogs in plural, and according to R. Elazar Aharon only raised one frog and that frog raised the other frogs by calling them.

I don't understand this explanation because the Gemara quotes R. Elazar as strongly rejecting R. Akiva's explanation--which the commentators explain, as above--and no early source implies that there is a similar reason to reject R. Elazar's explanation. Besides which, even according to R. Akiva Aharon only raised one frog and it was other people who hit the frog and caused it to muliply. Maybe I'm missing something.

Is anyone aware of a satisfying explanation of this Rashi?