This is a long tradition - it is a ruling by the Rabbis, going back centuries - till at least the time of the Crusades.
Jews are not allowed to approach the site which belonged to the Temple, apparently because they might offer prayers in the wrong place, or tread on the Holy of Holys. This ruling is expected to stay in place until the Messiah returns.
Israeli rabbinical councils have reaffirmed the “no prayer at Temple Mount” several times.
That’s a little different question that concerns being on the Temple Mount at all, not about prayers.
http://jcpa.org/jpsr/s99-yc.htm
“THE POLITICAL ROLE OF THE ISRAELI CHIEF RABBINATE IN THE TEMPLE MOUNT QUESTION”
I see. I thought it was a concession to Islam. How little I know.
Returns?
“Jews are not allowed to approach the site which belonged to the Temple, apparently because they might offer prayers in the wrong place, or tread on the Holy of Holys. This ruling is expected to stay in place until the Messiah returns.”
The first time Messiah came, few listened and He was crucified for the sins of the world. He returned in judgment in 70 AD, using the armies of Rome to execute that judgment, just as He foretold before His death.
He told both His disciples and the religious leaders that He would send messengers to the “lost sheep of Israel”, but that the religious leaders would persecute them; drive them from the synagogues and kill them. He said He would hold those in that generation responsible. And He did so, just as God had done as recorded in II Chronicles 36:15-22. Instead of using Babylon and Nebuchadnezzar, Christ used Rome and Titus. The parallels are all there for people to see if they are interested.