Question: In all the Highlander movies and in this show, was there any reason given why immortals can't fight each other on holy ground?
Answer: Not directly. But there is a penalty involved. In Highlander 3 the fighting on holy ground resulted in the destruction of one of the weapons. In End Game several immortals are murdered whilst on holy ground but no repercussions were ever revealed, so it's possible it is specifically about the fighting. Nobody knows what happens when an immortal is killed in a duel on holy ground but it's safe to assume the penalty will be severe because all immortals respect this rule, even the most evil ones (except that one moment in Highlander 3).
Answer: In the episode "Little Tin God," Joe Dawson mentions a duel between immortals on a temple in Pompeii—just before Vesuvius erupted. Whether the two are supposed To Be connected is up for debate, but still.