Here is the famous statement that by the bronze snake, it was not the snake (Nechushtan) which healed, but the focus of the Bnei Yisrael on their Father in Heaven. So too in the battle against Amalek, it was not Moshe's uplifted hands, but rather the focus caused by Moshe's uplifted hands, that the Bnei Yisrael focused on their Father in heaven.
Finally, a cheresh, shotah or katan, who don't have the requisite daas, cannot blow.
Is there any connection between the midrash and the surrounding dinim? I can spot three possibilities.
(1) Taking the simplest explanation, rather than that proposed in the gemara, we actually need thought and intent to fulfill the mitzvah. This is not some magic ritual which wins the day for us, but intent is required, because the entire purpose it to direct us to our Father in heaven.
(2) Taking the explanation of the gemara, that no intent is required. As a result, we might mistakenly believe that fulfilling the strict dictates of the commandment are all that is required. Hear the 9 blasts, or now, the 30 blasts or 100 blasts, and you are set. But this would be missing the point. Yes, it is important to fulfill the mitzvah because it is a mitzvah, but to fulfill the ratzon haBorei, and perhaps to end up with a good result, fulfilling the literal dictates of the mitzvah is not enough. As it states in Amos 3:6:
|ו אִם-יִתָּקַע שׁוֹפָר בְּעִיר, וְעָם לֹא יֶחֱרָדוּ; אִם-תִּהְיֶה רָעָה בְּעִיר, וַה' לֹא עָשָׂה.||6 Shall the horn be blown in a city, and the people not tremble? Shall evil befall a city, and the LORD hath not done it?|
That might be a trumpet of war, rather than a ritual shofar, yet it expresses the idea, that the purpose is that people will take it to heart and tremble, and do teshuva.
(3) There is a matching-up of the words im kiven libo in the first Mishna with umechavnin et libam in the second Mishna. This is then a peirush of the words im kiven libo. Then, insert the sentiments of (1) and (2).
This Rosh Hashanah, may we not only fulfill the requirements of a kosher shofar-blowing and hearing, but may we take it to heart, and turn our hears to Avinu she-ba-shamayim, and may this taking to heart accomplish what it is meant to accomplish.