You are assuming that "eat" and "edible", for example, share a common synchronic morpheme, which is a hallmark of the SPE analysis of English. There are innumerable problems with that analysis, which are a result of having pretty low standards for synchronic relatedness. An alternative, which has worked out pretty well for phonology, is simply to say that these words, along with pairs like "father" and "paternal", are semantically related (there is some connection in meaning) and historically related (they do derive fromt he same Indo-European root), but within the confines of a grammar, they are not related.
There are a number of devices employed in the SPE analysis to account for irregular phonological alternations. For example (see p. 201) the vowel alternation of sit ~ sat is subsumed under general vowel shift (which otherwise only affects tense vowels) because some verbs have the diacritic [+F] assigned in the past tense, and they expand the rule to include the context "[___,+F]" (i.e. "when a vowel is marked [+F]"). See chapter 4 in general for segmental analysis. The indices of SPE are very helpful for understanding this: there are word and affix indices, so if you want to know the SPE treatment of -ion, it's in the index and you can see the 9 citations of that affix.
The distinction between phonologically-neutral affixes (-ness, -able) and those that cause changes (-ity, -ous) is the foundation on which level-ordered phonology and morphology (a.k.a. "Lexical Phonology") is built. It has something to do with generality and productiveness – these changes are not productive or, it is often argued, only marginally part of synchronic English phonlogy, and marginal affixes have marginal phonological processes, because those processes were phonological rules many hundreds of years ago, and the results of those sound changes along with the conditioning affixation was long ago stuffed and mounted in the museum of sound change that is the lexicon of English.