|Temple at Tulum in Mexico|
The Book of Mormon recording places the discourse at the Temple in Bountiful. The Savior could have chosen anywhere to bring his new covenant to the Nephites. It is significant that he chose to come to a temple!
Actually, the idea of the sermon emphasizing the temple isn't that far off from the New Testament, either. While I believe the sermon could have been delivered at a mountain in the Galilee, I think there is a symbolic element to the title as well. In the Old Testament, the term Mount, Mountains, and Mount Zion all became synonymous with a temple. It was felt that a mountain was where a man could go to come to God's presence, and that the pinnacle of the mount was where God comes down to join with man on earth. In fact, it was on a mountain top where Moses had his temple-like experience.
The term Sermon on the Mount may in actuality, regardless of where it was physically delivered, refer to a temple sermon. In other words, it was (and still is) a sermon meant to prepare people to enter into a covenant with God.
This is born out when we compare it to 3 Nephi. Before the Savior starts the famous discourse, he teaches the disciples about baptism, as found in the end of Chapter 11. Then, when he starts the discourse which was delivered to all the multitude, he started it off again by emphasizing the importance of baptism.
As we know, it is baptism that is the covenant we make with God for him to bring us home. The rest of the sermon, then, can be viewed as a temple prep class--a discourse about how we can better make and keep our covenants.