In many yeshivot and shuls with a yeshivish crowd, the chazzan for mussaf on Rosh Hashanah and Yom Kippur does not say the full Hineni out loud. Instead, he says all the parts talking about himself quietly and most of the parts talking about the congregation out loud.
According to all the Rabbis and chazzanim I have asked, the reason is that it can seem haughty to publicly proclaim "look how unworthy I am, but I'm going to do it anyway." (It brings to mind the classic joke about two students in Novardok yelling at a third because "who does he think he is to be a gor nisht!?")
However, none of them could point me to any source where this practice appears in writing or any information about who started it and when.
Does anyone know of a source for this practice?