I cannot speak (entirely) about how rare it is. Nor can I speak about any midrashic analysis of it. However, I can address what causes it.
The pashta is a pausal trup sign that splits in half a clause that ends in zakef. Where two occur, first the first one divides, then the second one divides. This division usually occurs on the basis of syntax, such as whether an object, subject, verb, or preposition leads the clause. See William Wickes for a full discussion of this.
In the pasuk in question:
וְהָיָ֗ה הָאִישׁ֙ אֲשֶׁ֤ר לֹֽא־יִשְׁמַע֙ אֶל־דְּבָרַ֔י אֲשֶׁ֥ר יְדַבֵּ֖ר בִּשְׁמִ֑י אָֽנֹכִ֖י אֶדְרֹ֥שׁ מֵֽעִמּֽוֹ׃
looking only at the first half, up to the etnachta, we have:
וְהָיָ֗ה הָאִישׁ֙ אֲשֶׁ֤ר לֹֽא־יִשְׁמַע֙ אֶל־דְּבָרַ֔י אֲשֶׁ֥ר יְדַבֵּ֖ר בִּשְׁמִ֑י
The trup symbol at play that divides something ending in etnachta is the zakef on Devaray and the tipcha on yedaber. Thus, it is divided into:
וְהָיָ֗ה הָאִישׁ֙ אֲשֶׁ֤ר לֹֽא־יִשְׁמַע֙ אֶל־דְּבָרַ֔י
אֲשֶׁ֥ר יְדַבֵּ֖ר בִּשְׁמִ֑י
and the second part of that is divided into:
אֲשֶׁ֥ר יְדַבֵּ֖ר
בִּשְׁמִ֑י
In terms of the first half, the revii and pashta(s) both divide something ending in zakef. And so, the clause:
וְהָיָ֗ה הָאִישׁ֙ אֲשֶׁ֤ר לֹֽא־יִשְׁמַע֙ אֶל־דְּבָרַ֔י
is divided into:
וְהָיָ֗ה
הָאִישׁ֙ אֲשֶׁ֤ר לֹֽא־יִשְׁמַע֙ אֶל־דְּבָרַ֔י
and the latter part is divided into:
הָאִישׁ֙
אֲשֶׁ֤ר לֹֽא־יִשְׁמַע֙ אֶל־דְּבָרַ֔י
and the latter part is divided into:
אֲשֶׁ֤ר לֹֽא־יִשְׁמַע֙
אֶל־דְּבָרַ֔י
The clause keeps getting divided off at the start, for syntactic reasons Wickes discusses.
Now, the general rule of dividing a clause ending in zakef (see in Wickes) is that the symbol used to divide is a pashta close to the zakef, and a revii further from the zakef. That is:
1 word before: Pashta
2 words before: most frequently Pashta, but Revii admissable
3 words before: most frequently Revii, but Pashta admissable
4 or more words before: must be revii
However, from a musical standpoint, a series of Reviis will not stand in certain circumstances, and so they will "transform" into Pashtas. This is what is happening in the present instance. To cite Wickes:

While I don't possess statistics as to the frequency of this pattern (there is some software out there that will indeed tell you), note that Wickes mentions that "examples of this transformation are (as we should expect) much more numerous than those in which R'bhia remains."
At the end of the day, since this is a perfectly normal pattern predicted by the rules of trup and subject to a specific syntactic structure of the sentence, I would expect this pattern to occur on occasion. And I would see no need to seek out midrashic explanation.