So, why couldn't we use the prefix trick with the {-'egh} and {-chuq} ?Mostly because of the rule that says they only allow no-object prefixes. But we have one canon violation of that rule, in paq'batlh: quv HIja'chuq Don't speak to me of honor!
Some people question the strength of this as an example, though, because ja'chuq appears in the dictionary as a lexicalized word, so this may be an example of a root+prefix that has fossilized into its own root.