One of the major focal points of the prayer service on Rosh HaShana is the mussaf amida containing blessings with the three themes of malchiyos, zichronos and shofaros. The Talmud (Rosh HaShana 34b) tells us that HKB"H tells us: "Recite before me malchiyos, zichronos and shofaros: Malchiyos - so that you shall coronate me as your King. Zichronos - so that your remembrance comes before me for the good. And with what? With the shofar." Notably, even though each theme has its own beracha the Talmud seems to explain the reason for the first two berachot directly. The third beracha is mentioned only in a secondary way - "With what? With the shofar." This seems to be an explanation of why we blow the shofar. Why isn't the purpose of the beracha of shofaros more explicitly stated?
Furthermore, when we analyze the text of the three berachos, we see that the first, concerning malchiyos, clearly focuses on coronating Hashem as our King. The second clearly focuses on G-d remembering our actions. The third, though, focuses on G-d revealing His presence in the world starting at Har Sinai. Why doesn't the Gemara spell out this theme rather than just vaguely referencing the shofar?
In addition, each beracha contains three verses from the Torah, three from Tehillim, and three from Nevi'im. In the beracha of shofaros, which, as mentioned, focuses on Revelation, the first three pesukim from the Torah focus on the Revelation of Sinai punctuated by the sound of the shofar. The last three highlight the Revelation of the final redemption also accentuated by shofar blasts. But the middle three p'sukim from Tehillim do not seem to focus on Revelation. One verse speaks of the shofar on Rosh HaShana, "tik'u bachodesh shofar bakesseh l'yom chageinu." One speaks of G-d being elevated with the shofar, "alah Elokim bitru'ah, Hashem b'kol shofar." The final ones of this section, taken from the last psalm, speak of many musical instruments being used to praise Hashem including shofar. How are these verses related and how do they relate to the general theme of Revelation?
Rav Soloveitchik (Yemei Zikaron, "Alei T'eina, v'Kosnos Or") beautifully explains that the pesukim from Tehillim focus on the revelation of Hashem on Rosh HaShana itself. G-d reveals himself to the penitent encouraging him, embracing him, awaiting his return. Elsewhere, (seen in Nifla'os HaRav) Rav Soloveitchik explains that the Torah's statement of "us'machtem lifnei Hashem Elokeichem" indicates that true joy occurs only when in the presence of G-d. The fear of judgment of Rosh HaShana eliminates the ability to recite Hallel which would ordinarily reflect this joy (Arachin 10b). Nonetheless, a hidden Hallel is indeed recited through the verses from the last mizmor of Tehillim indicating all the instruments including the shofar being used to praise Hashem. According to the Rav, then, all of the pesukim do indeed focus on the theme of Revelation.
Based on this idea, perhaps we can answer our other questions as well. The Gemara states "Bameh? Bashofar!" Perhaps the Gemara is referring to both the blessings of malchiyos and zichoronos. How are we to coronate G-d? How are we to assure that Hashem remembers us l'tova? The Gemara answers: with the shofar! The shofar represents G-d's revelation to us. But this revelation was not only to be punctuated in the historical record at its endpoints - at Har Sinai at the beginning of Jewish national history and at the Final Redemption, the last stage of Jewish history. It is also a constant one on both the national and individual levels. G-d constantly reveals himself to us in our lives by exercising His Divine providence over us. His constant knowledge of every, even minute, aspect of our lives, constantly monitoring, modifying, and re-creating all of our life pathways reflect His constant intense connection to us. To be sure, the intensity of the connection to HKB"H depends on our spiritual level, but Hashem's connection to everyone is a given. How are we to coronate G-d, to recognize Him as the ruler of not only the world but also to realize that the entire purpose of our existence is to connect to Him? How are we to assure that we are remembered for the good before the Heavenly court? Bashofar, through being aware of G-d's constant presence in our lives. Not to get caught up in the havlei haz'man which tend to numb ourselves to this awareness of G-d's presence in our lives. The shofar wakes us up (Rambam Hichos Teshuva), breaks down the barriers (Michtav Me'Eliyahu as per the shofar of Yericho) and allows us to start on our journey to return.
The Haftorah for Shabbos Shuva begins "Shuva Yisrael ad Hashem Elokecha - Return Israel to Hashem, your G-d!" Rather than viewing the return as a journey toward G-d, perhaps we can characterize this as a return inward to that which is already there, to G-d's constant connection to us which we are not taking full advantage of. May we all "re-sign" on the b'ris with HKB"H on Rosh HaShana and may the awareness of His constant presence carry us through a sweet new year!