Sacred prostitution or rather temple prostitution has seemingly originated in Mesopotamian culture and has been observed in various idol worship culture of Ancient Egypt, Mid-east, Greece/ Rome, India, China and even in Japan...
However amongst Monotheistic population this isn't well documented... What are the possible reasons for the same..? Lack of documentation or lack of public support for the ritual of temple prostitution..?
You're starting with an incorrect premise, I'm afraid! There is in fact very little evidence for sacred prostitution in Mesopotamia or Egypt outside of the notoriously unreliable Herodotus. As Stephanie Budin wrote in Women in Antiquity,
One interminable debate in Near Eastern studies that will continue long after the sun has swallowed the rest of the solar system is the matter of prostitution... In short, the Mesopotamians did not write much - anything - about the profession of prostitution. This absolute lack of data, however, has not in any way restrained a century's worth of Assyriologists inter alia from writing reams about the Whore of Babylon and her horde of whore minions. For decades, almost every professional title ascribed to a female in either Sumerian or Akkadian was translated as "(sacred) prostitute," apparently on the grounds that women could serve no other function in the business world...
There is always more to be said on this topic, but u/Naugrith discussed the slim evidence for sacred prostitution in How were Sacred Prostitutes selected in Ancient Times?