Although it would not follow the historical precedent of the temple on the Temple Mount, why couldn’t the Israelis find a new site and build a new temple in Jerusalem.
For example, build up an area next to the Temple Mount along the Wailing Wall and build it to a height slightly above the Temple Mount. Eventually it would be known as the Temple Mount after a couple of thousand years, give or take.
Isiah 66:1 This is what the LORD says (to David): "Heaven is my throne, and the earth is my footstool. Where is the house you will build for me? Where will my resting place be?
David built the Temple so that God would have a place to rest on Earth. That place is the holiest site for Judaism and is the very basis for its structure. Jews are still forbidden today to walk above on the Temple Mount because that is where God's Spirit had taken up to rest as signs in several languages give ample warning to all. God's resting place is what anchors the Temple and which is its raison d'etre for having been constructed.
Where is this specific site where the Jewish God rested?? It's the exact same spot where these G-d dammed misbegotten Muslims decided to build their Whore house of prayer, the Dome of The Rock, exactly right on top of the spot where the Jewish God's Spirit rested.
So, if you want a Jewish Temple that exists, is built according to the specifications, protocols in which God's Spirit would rest as it did in the previous two Temples, you're not going to build it in Short Hills, New Jersey, just like you won't build a Lincoln Memorial in Astana, Kazakhstan, it's capital city.