Even though this altar was dedicated in the name of the entire nation, each of the twelve tribes was individually represented by a separate monument. Thus, each tribe became obligated to accept total responsibility for the fulfillment of the entire Torah, rather than sharing that responsibility with the other tribes. Hashem has chosen to maintain the individuality of each tribe, so that each one continues to view itself as sustainers of the Covenant with Hashem.
Horav Avigdor Miller, Shlita, suggests two additional reasons for maintaining the distinct status of each tribe. First, Hashem imbued each tribe with unique characteristics, which constituted its own contribution to the perfection of Klal Yisrael. Each maintained its own territory and asserted its own identity. Each tribe intermarried within that tribe thus enhancing its particular personality traits. By sustaining its distinctiveness, the tribes aimed to achieve greater perfection of the entire collective unit, Bnei Yisrael.
Another advantage of preserving the individual status of each tribe was to exclude the influence of dissidents. A united people may be vulnerable to the seductive powers of a charismatic innovator. For example, when Yeravam ben Nevat seized power over the Ten Tribes, the remaining tribes of Yehudah and Binyamin continued to be loyal. They, therefore, endured until today, even after the others were lost. This was possible only because these tribes possessed independence as a result of their individual status and territorial integrity.