The Deutoronomists worked tirelessly to promote Jerusalem and its temple. One of the main features is the idea of one (dominant) god and one central temple to worship that God. But the Duetoronomist’s early writings were in a time when Jerusalem was the lone fortified city to have withstood the Assyrain assualt. It was a golden age for the city, with no rivals nearby in material wealth. As time went by rivals like Shechem reappeared, as well as smaller towns as cultic centers. 
Introductions to religion are rife with the idea that cultures moved toward monotheism from polytheism and that the OT demonstrates this change. But archeology and the history of the Hasmonean rise to power paints a very different picture. 
In Elaphantine we see letters talking about rebuilding temples, plural, with no awkwardness that would suggest anyone thinks there should only be one temple. In Qumrun we have a people calling themselves to purity but rejecting the Jerusalem Temple as authoritative. In Mattathias we have an echo of Josiah 450 years later. No progress. The Hasmoneans will destroy the temple in Shechem, the temple of the Tobiads, and another temple in Egypt will stand in which YHWH can be worshipped. 
What we have in 160 BC seems little different from the pain of 586 BC, with the local temple and its god being shamed by a foreign power. Notice this did not enrage the surrounding cities and villages to come to the rescue of Jerusalem. Some of these towns would house those fleeing the rage of Mattathias as he sought to reestablish his ancestral customs. YHWH, or Zues or Apollo, could be worshipped anywhere, not just Jerusalem. As a matter of fact the first man killed by Mattathias was in a hill country village as the man went to address the altar in the manner shown by a Greek priest imported to show the customs. This altar was not in Jerusalem. It was in a local village, which would have its own village leader to perform the rituals. 
So the Duetoronomist did not represent a shift in theology, a centralization of geography to mirror a centralization of deity. His world was one were Jerusalem reigned supreme in the highland. It made sense that THAT temple was special.