Some aspects of it happen to overlap with why I like the Southern Conjecture. Arguably this could still fit the Muslim Holy sites being the Outer Court trodden under foot by the Gentiles in Revelation 11.
I also think of 1 Kings 11:7, where on a Hill outside of Jerusalem is where Solomon latter built a High Place for Chemosh and Moloch. Some translations say this Hill was "east of Jerusalem", but the KJV simply says "in the hill that is before Jerusalem". The current traditional Temple Mount is north of the City of David. (Udpate: I'm now aware most scholars think that is the Mount of Olives.)
The theory was around before Conruke and Missler recently jumped onto it. Here is an article critical of it from a site that supports the Al-Kas fountain view.
One aspect of the debate over The Temple's location I feel gets overlooked is this. The Tabernacle David placed The Ark in when he first made Jerusalem his capital is NOT the exact same plot of land The Temple of Solomon was built on. David did not buy the threshing floor on Mount Moriah until after the Plague following his Census, which was late in his reign after Absalom was dead already. The Ark remained in that earlier Tabernacle until The Temple was complete.
Another thing over looked from II Samuel 24:23 is that Aruanah was a King. " All these things did Araunah, as a king, give unto the king. And Araunah said unto the king, The LORD thy God accept thee." Wikipedia says that English translations try to obscure or confuse this fact. But I feel it's apparent enough in the KJV as I just quoted. So I'm not sure the assumption that this land must be within what David originally conquered is as solid as Cornuke and others think.
Descriptions of the Future Messianic Temple tell us nothing about the Location of Solomon's Temple, or geography as we know it at all. Ezekiel has a very different Geography for the entire region, and his Temple is miles North of Jerusalem not within it. I'm attracted to the view that Ezekiel's Temple is actually on on near Shechem or Shiloh. So it annoys me they spend so much time quoting from the last 9 chapters of Ezekiel and related Prophecies.
And one has to be careful doing a word study of Zion as well. Zion became very much a poetic name rather then a technical term. Anytime the borders of Jerusalem grew, that too became Zion. Then there is the Heavenly Zion of Psalm 48 which will descend as New Jerusalem.
I also feel the Southern Conjecture is consistent with Jesus saying not one Stone would be left. As the diagrams of it show, the wailing wall in that view is not one of The Temple's wall.
The link I provided critical of this view agrees that the Antonia fortress was built on the Temple mount. And it was all Roman construction after the Bar Kochba Revolt, when Hadrian's Temple complex was build.
Something else I'm thinking about. All these debates about the Temple's Ancient Location get brought into theories eschatologically about how the Third Temple which The Man of Sin will desecrate gets built. But I'm thinking lately, what guarantee is there that Temple will even be built on the accurate place?
Jesus said the Abomination of Desolation will stand in the Holy Place. Some might insist he wouldn't have worded it that way if it wasn't the authentic site of Solomon's Holy Place. But the Holy Place is just a title for the innermost sanctum of The Tabernacle originally, which was portable. It is believed at some point after Solomon it was decreed it can't move again, but as I've said I don't believe the even further future Ezekiel Temple is on the same location. The 70th Week Temple I believe must stand in Jerusalem, the same city The Two Witnesses will preach from in Revelation 11. But maybe not exactly where the old ones where located.
And I've seen some theories say the Second Temple wasn't actually on the exact same site as Solomon's.
I'll have to think over this for awhile.