I'm not sure that the issue with enormity is that it has emotional baggage. The issue is that it has restricted usage -- it is only use in certain constructions such as "enormity of the crime". This is not a matter of emotional baggage so much as simply an accident of the development of standard usage.
Other words with similarly restricted usage include: nether, bated, riddance, and petard. There is a list of some such words in the Wikipedia entry on Fossil words: https://en.wikipedia.org/wiki/Fossil_word. These fossil words are perhaps a more restricted case than "enormity" since most of them occur only in a single idiom. But I think the same general idea applies: they are words that continue to be used only in restricted cases and limited constructions.
As for emotional baggage, many words can have emotional baggage, but mostly it depends on the context in which they are used. There are, of course, some trigger words that set off an instant response no matter how they are used. Some of these are durable. Some lose their trigger status after the events they are associated with fade from consciousness. If you Google for "trigger words" you will find lots of lists, though they seem to focus on the ones to use rather than the ones to avoid.
In any case, while individual words can have emotional overtones, to really evoke emotions you need to tell a story. This can be a very brief story, using only a few words, but it is stories, not words, that pack real emotional punch. Indeed, to the extent that words have emotional overtones it is because they trigger a memory of stories.
The other thing about using a story to evoke emotion rather than a word is that a story is a much more accurate instrument for the job. The emotional overtones of words can be all over the map, because they can suggest different stories to different people. By telling a story, you control which story the reader receives and therefore control the emotional response much more.