In Deuteronomy 12:1-9, there are instructions regarding things that the Israelites were to change in their worship of God whenever they came into the land. (Deuteronomy was written just shortly before they began to take over the land.)
"Do not blend the worship of Me with idolatry—with something that is foreign to My nature; something that is foreign from or different from My plan, My purpose, My way."
That place became Jerusalem. It was not there at first. It was at a couple of other places, the most noteworthy being Shiloh. But wherever God placed the tabernacle and then the temple, that is where His name was. That was the center of worship.
Why did God want these places destroyed? Because He wanted there to be no temptation to idolatry; no joining together of the way the people of the land worshipped their god with the way God wanted His people to worship Him. He did not want His way to be diluted by anything that was foreign to His purpose, to His plan. So He specifically designates that there is to be only one place.
As we just read there in the book of Deuteronomy 12:8-9, Moses told the people, "You shall not do as we are doing here today—every man doing what is right in his own eyes," as they crossed over into the Jordan. From that point forward, they should have been coming into the place of rest. They should have been finding the peace that God would give them, which comes with His blessing in the land of promise and peace for those who would obey His voice. It was truly the land of peace that comes from living the Word of God.