Remember, it's an equilibrium relation
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Local in what sense? (I don't mean to push you on this and am happy to stop here if you prefer.)
I just meant what I took you to informally mean by "following photons". Not literally of course, but I meant thinking locally about energy flows, and reconciling with the global picture.
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A nice alternative simplification emerges if you treat the outer (GHG) layer as reflective instead of absorptive. Then it's clear why both emissivity and absorptivity decrease, because photons can't get out or in, resp
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Absorption is trickier, but in the simplest case where all properties are wavelength independent and there is structural symmetry, reemission happens in both directions, so it's like a 50 percent reflection, and the reflection picture works
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