The abstract analysis is not actually Hayes' own analysis, but was proposed by Chomsky and Halle in The Sound Pattern of English. The number of phonologists who actually accept this analysis surely hovers around zero. I don't know about Hayes, but when this analysis is discussed, it's generally understood that the analysis is wrong, and the reason for even mentioning it is to make some methodological point about why we should reject such a silly proposal. I'm not even sure that Chomsky and Halle themselves didn't have their tongues in their cheeks when they proposed it.
Even in SPE, the analysis is not proposed as a way to describe ordinary English forms, but only for certain exceptional English forms. C&H compare several ways of describing forms that are irregular in the sense that they do not conform to the rules that C&H have developed for describing the great majority of English words, and conclude that the abstract representations are the most economical way of describing such irregular forms.
Overall, the SPE analysis of English proposes that at the deepest level -- the lexical level, I suppose -- English words have no stresses marked, and all stresses are assigned by phonological rules. This is mistaken, but it is a reasonable idea, since there are regularities in the English stress system, and in a theory that describes phonological regularities with phonological rules, it seems to follow that stresses should be assigned by phonological rules.
Actually, it doesn't follow. We can have some stresses assigned lexically, and others assigned by rules. In general, morphophonemic rules affect parts of pronunciation that are lexically assigned (a reasonably clear case is the Backness Harmony rule of Turkish), and English stress is phonologically morphophonemic. Stress is phonemic, but it can also be assigned (or perhaps changed) by phonological rules of English.
There is a complication in English that makes this difficult to see, which is that English stress assignment is dissimilatory, like the stress in other alternating stress systems. I discussed this briefly earlier, in another answer here (see answer #7).
So, in my view, the difference between English "baron" with regular stress on the first syllable and "baton", with irregular stress on the second syllable, is appropriately described by assigning phonemic forms with the stresses as observed. The SPE Main Stress Rule is dissimilatory, so that it cannot assign the main stress to a syllable which is followed by a stressed syllable, and that's why it can't apply to the first syllable of "baton". The stress of "baton" is irregular, because if the stress were not known to an English speaker, the Main Stress Rule would make the first syllable stressed, rather than the second syllable.