I’ve never personally encountered a sutta or later text suggesting this, but it seems somewhat plausible to me that the order in which the khandhas are listed is in order of increasing subtleness of our attachment to them. Allow me to lay it out:
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Rupa. The khandha most obviously not-self. Even outside of Indian or Buddhist thought, one encounters statements such as “You are not a body. You are a soul which has a body.” The body also is made up of the same matter as that which surrounds it. It often develops problems that are entirely out of an individual’s control, e.g. sickness, aging and so forth. Relative to the other khandhas, it’s much easier to see that we’re not really the body.
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Vedana. Because vedana is mental, it feels more immediately personal than rupa. But, in comparison to the other mental khandhas, it is much more obvious that it is out of our control: Certain sense contacts feel pleasurable and others painful and we can’t chose how they feel or not to experience them.
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Sanna. The operation of sanna is less obvious than that of vedana. I suspect that without an encounter with Buddhism (or another tradition that analyzes the mind similarly), most people would never realize that our perceptions are separate from sense-consciousness. However, once that distinction is made clear, it is fairly straightforward to see that sanna is a mostly automatic process that occurs upon phassa and we have little direct control over the nature of those perceptions.
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Sankhara. Because sankhara is tied to volition, its activities feel extremely personal in comparison to sanna and vedana, e.g. “These are my thoughts.” or “These are my choices.” It is rather challenging to maintain a belief and perception of an existent self while not seeing “the do-er” as a core part of that self. Whereas with the previous khandas, one might develop a partial understanding of those khandhas as anatta merely by thinking and reflecting upon them, to gain insight into sankhara as anatta, one generally needs direct meditative experience to see how sankharas are conditioned (e.g. seeing how “the thoughts think themselves”). Unlike sanna and vedana, sankhara does not merely occur mechanistically upon phassa.
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Vinnana Clearly the most subtle of all khandhas in regard to our attachments to them. Awareness seems almost identical to who we are and it is counter-intuitive to understand that there is knowing without a knower. Consciousness also is much more stable than other khandhas because even if the objects of consciousness change, the fact of knowing an object of consciousness generally remains. Because of this, even within Buddhist circles that base their doctrine on the Pali Suttas, there are many well-regarded teachers who basically expound an understanding of dhamma in which one attaches to-- and takes refuge in awareness, rather than developing dispassion and non-attachment towards it.
I hope I have managed to somewhat clearly lay out the increasing subtleness of each khandha! I am quite curious if people have encountered this concept elsewhere and whether they think its generally plausible.