Could it be a question of phonetics? In wouldn't, we know that we have to insert a "schwa" or "mid central vowel", IPA ə, i.e. the most non-descript vowel possible, and very common in English, somewhere.
In wouldn't this sound doesn't actually come where the apostrophe is, but instead between the d and the n. The reason for putting it where it is references the fact of omitting the O sound and/or the letter O.
Ham 'n eggs is good because, if the apostrophe corresponds to the schwa, it is also where the schwa actually goes. But you could potentially achieve the same effect with Ham n' eggs.
If you try to go Ham 'n' eggs, however, two problems are created: lexicographically, it starts to look like "n" is quoted rather than being preceded and followed by phonetic markers. Phonetically you might be tempted to think that it's pronounced "ham ənə eggs", which would be seriously funny and potentially rather Italian.