With the Temple gone, the Beit Knessets/Synagogues have arrived. But on which basis (verses) are they established and which functions, tasks, goals or purposes of the original Temple do they fulfill?
The notion of Bate Knessiot and Bate Midrashot, house of prayer and house of study is independent. The notion of Bet Mikdash is for sacrifices and prayers, but not prior. When Bet Hamikdash was destroyed, nothing really replace it, but BK and BM became all our patrimony, and Tefila and Torah study became occupations that replace Avoda. See Rabenu Yona on the 2nd Mishna of Avot for a good explanation about Tefila replacing Avoda. Chazal also said that learning Hilchot Korbanot plays the role of Korbanot. So today, places of prayer and learning are a kind of substitute of Mikdash. But the purpose was not to create a "new kind" of house.