Upvote:3
The location and time period of Tel Arad seems most similar to the "high places" that the book of II Kings credits King Josiah of Judah with eliminating in favor of a single temple under royal supervision in Jerusalem. It is not clear whether these places were used for the worship of Y-H-V-H, for idolatry, or for a syncretic mixed practice.
Reportedly, there were also temples to Y-H-V-H established at Dan and Bethel by Jeroboam ben Nabat. Archeologists have found evidence for a cultic site at Dan, although the location of the one at Bethel remains elusive. The book of Kings claims that these were set up with a political motivation, to offer an alternative to people wanting to cross the border from the Northern Kingdom of Israel into the the Southern Kingdom of Judah to sacrifice at a temple. As Israel became a prosperous country under the House of Omri, these temples flourished. The writers of Kings and Chronicles emphasize how idolatry took over those temples, but various prophets make the same statement about both the high places and even the temple in Jerusalem.
After the Babylonian Exile, temples for the worship of Y-H-V-H sprung up in a few places. In Leontopolis and Elephantine in Egypt, temples were established that offered sacrifices. The Samaritans offered sacrifices on Mount Gerizim, as they continue to do to this day. These were declared illegitimate by the rabbis as Rabbinic Judaism replaced sacrifice-oriented Biblical Judaism after the destruction of the Second Temple in 70 CE. It became an accepted principle that sacrifices could now only legitimately take place on the Temple Mount in Jerusalem, which was now impossible, although lawful sacrifices had taken place previously at other sites like in the desert and at Shiloh.
Synagogues grew up parallel to, and in some ways independent of, the sacrificial system. "Synagogue" is the Greek translation of the Hebrew "Beit Midrash", meaning house of study. They have no exact equivalent in other cultures of antiquity, although they could be seen as similar to the academies of Greek philosophic societies. They were places where Jews could gather and study the Torah and the Prophets. After the fall of the Second Temple, they gained greater importance in the continued survival of Judaism and the Jewish people. Prayer and study were conceived as a replacement for the now-impossible sacrifice in the Temple of Jerusalem. The synagogue thus became the focus of Jewish life to this day.
To answer your specific question, the synagogue was not originally intended as an equivalent to the Temple, but it became its replacement through force of events and an evolution in Jewish theology.