Inspired by this question.
We know (Pesachim 56b) that Baruch Sheim, at least according to one explanation, is a tefillah Moshe heard from the Malachim. Thus, we only say it out loud when we're on the level of Malachim.
Yet, we (by that I mean the minhag in my community* - not sure whether this is true everywhere) say Baruch Sheim out loud after messing up a bracha beyond the point of "lamdeini chukecha." If we're not on the level of malachim, why should we be allowed to do so?
*Note that my community is primarily formed of talmidim of R' Weinberg of Ner Yisrael fame.