I understand there are other issues here beyond the machloket:
1) where is prohibited area. It seems that modern archaeology can rule out some areas not being in the mikdash. Just make sure those who make determination are not motivated by politics. I did not see charedi poskim addressing this issue, do they? maybe they do not think that current archeology reached definite conclusions.
2) political implications aggravating not just the locals, but a billion of Muslims worldwide. This seems the main factor for the negative psak … Position to ignore that billion is definitely political and , while understandable, is very risky and should not be in hands of some crazies who can’t even get to Knesset on their own.