Ok, so what stands out to me is at each of those levels you can define an individual of sorts (proton, phenotype, society, meme) with goals (electromagnetic, genetic survival, ??, memetic survival). So I get what you mean that definition of goals (quality) goes hand in hand with definition of individual and therefore subject/object in this restricted model of reality.
But that's what this model seems to be to me, more of an ELI5 explanation than the grown up one. "the proton wants to move towards the electron, the rabbit wants to have babies, etc" is a simplified model that leverages our brain's skill at modelling motivations of other animals but falls prey to our tendency to see such motivation where it doesn't exist. Once you start testing this model by making predictions, it doesn't work because the levels work rather differently under the hood. Try using evolutionary principles at the social level to predict the growth of New York for example, and you are going to mispredict because New York isn't going to reproduce in any meaningful sense, it will either grow or die (there's a vague parallel to group selection controversies here but not that relevant). People (like the inhabitants of New York) and ideas (like ideas on how cities should be run), conversely, can be said to evolve due to mutation and reproduction and if you predict the growth of New York based on evolutionary influences from those levels you are more likely to succeed (alternatively you could take some sort of network/complexity approach but whatever works it isn't going to be city level evolution * ).
But let's not get hung up on evolution, it's just an example of how the levels differ so much in their details that the only correct overarching definition of quality for each level would appear to be "the thing the thing is going to do anyway", a definition so general as to be useless * . From that light the good student essay was the thing Phaedrus wanted (the standard he was trying to achieve in his students) but if we want theories to make useful predictions we need to predict when this will and won't happen (e.g. because the alcohol molecule's notion of 'quality' interferes with the student's brain's efforts to reproduce Phaedrus' notion thereof) which is where the model breaks down. Or maybe this theory isn't supposed to help predict anything but is supposed to help grade essays? but "what I wanted to see" is not a useful definition of quality for the student either.
*edit: unless it's morphic resonance a la Rupert Sheldrake, a theory so general you can state it as "whatever happens becomes more likely to happen again". But while at first sight that notion is strongly related to quality as defined by Pirsig, I think that may be an illusion caused by them both being super-general abstractions. MR is subtly different and although not accepted by scientific consensus that difference at least allows it to make testable predictions.
Thank you for helping me think through this stuff more (as my edit history would show!)