Someone told a gadol about his shalom bayis problems. The gadol told him, "The solution is to be mevater." The man replied, "Exactly. I tell my wife all the time that the solution is that she should be mevater, but she doesn't get it..." This demonstrates people's tendency to think that others have a problem, failing to realize that they might be the one at fault.
The Or HaMeir asks if the primary purpose of the shofar is to arouse people to teshuvah, why didn't the Torah instead instruct the Rabbanim of each beis medresh to deliver a fiery mussar drashah to rouse people to teshuvah? Why the shofar?
The Or HaMeir answers with a mashal: A town hired a man to stand guard on a mountaintop. If he noticed thieves or any other impending danger, his job was to ring bells, shout, and warn the townspeople below. Once, the guard saw thieves. He shouted and rang his bells: "Ganavim! Thieves!" The wealthy people frantically ran to save their properties, but the poorer folk weren’t worried. They knew that the thieves weren't after them. Another day, the guard shouted, "Fire! There's a fire!" This time, even the poor people ran to put out the fire because the fire could cause them financial loss.
The Or HaMeir explains that if the Rav of every congregation would give a mussar drashah instead of the shofar, people would say, "The Rav isn't talking to me. He is speaking to others who need to improve in those areas." For example, if the Rav would speak about the importance of studying Torah with hasmadah, some people would think, "I'm glad the Rav is speaking about this topic because there are many people in this beis medresh who should study more Torah." He doesn't think the drashah was intended for him. Whatever the Rav speaks about, be it tefillah, tzedakah, or middos, there will always be those who think the Rav is talking to others and not to them.
Therefore, the Torah tells us to blow the shofar. The shofar shouts, "There's a fire, and we're all in danger!" It is a call to action for everyone.