if the biblical temple had been there it would have had a water supply to clean up from the animal sacrifice. there is no water at the "temple mount" holy places command immense resepect and are accessible. they don't have fifty foot high walls to keep people out. the gathered faithful are all the protection they need. josephus the historian specifically mentions that the romans destroyed the temple down to the ground and it was impossible to see where it had stood. he makes no mention of fifty foot high walls remaining. the romans had a castle there called the fortress antonia which they used from the time of king herod to hundreds of years after the obliteration of the temple. this has never been found. not on trace. all over the roman empire there are the ruins of square or rectangular roman castles of similar dimensions to the temple mount. you are praying at the walls of a roman castle. there are multiple reasons why the biblical temple cannot have been at the site of the modern temple mount. not least the smell caused by animal sacrifice without running water would have been overpowering. it is just not reasonable to have expected anyone to have butchered animals there. they wouldn't have been able to get near for stench.
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