Because it doesn’t have to be rebuilt on where the Mosque is now. It only has to be rebuilt in Jerusalem. There is nothing in the Old Testament that decrees that the temple will be rebuilt over the Dome of the Rock...there is nothing that stops it other than God’s timing. A group of Orthodox rabbinnical students demonstrated that fact by laying a ceremonial corner stone “Next” to the wailing wall 18 years ago while pointing out that Torah doesn’t specifically state WHERE the temple SHOULD be built.. Caused a bit of fuss at the time!
Dome of the Rock. Revelation.
No traditional Jewish religious authority would accept any location but the exact site of the First and Second Temples. Period.
Since non-Jews would not be allowed on the Temple Mount, what would be the point of leaving Muslim shrines there?