The Beit Hamikdash does take center stage on the holiday of Pesach. This was the only one of the three pilgrimage festivals where the women also needed to appear. They also were commanded to partake of the קרבן פסח together with the men.
Many do not realize that the Beit Hamikdash had three other important functions aside from offering sacrifices. It was a place of Jewish unity, education and justice.
Despite the division of the land by tribes, the visit to Jerusalem brought about Jewish unity. If we consider that the מעשר שני or its monetary value needed to be consumed in Jerusalem, it certainly was shared by all of the pilgrims regardless of their tribe. This brought Jewish unity for sure.
The Levites fulfilled the role of educators. The Kohanim and Leviim only served two weeks out of the year. They were not given a portion of land in Israel. Their job was to educate and a large number of them served as judges.
Justice was served with the great Sanhedrin being located on the Temple Mount. The holiness of the place no doubt profoundly inspired the judges. They were certain to give correct judgement with such inspiration. Hence, the Temple united, educated, and helped bring about justice .