If you work through the math for CUPED, you'll see that only the aggregate correlation term can be interpreted as being "per-unit" -- all of the other terms in

If you work through the math for CUPED, you'll see that only the aggregate correlation term can be interpreted as being "per-unit" -- all of the other terms in the equation are the same terms you use in your post. Insofar as I think your intuition is leading you somewhere, I think it's leading you towards a realization that a "diff in diff" approach rather than regression adjustment can increase variance in some settings. But regression adjustment is provably better in essentially all circumstances: the only settings in which it is ever worse than no adjustment are outlined clearly in https://projecteuclid.org/journals/annals-of-applied-statistics/volume-7/issue-1/Agnostic-notes-on-regression-adjustments-to-experimental-data--Reexamining/10.1214/12-AOAS583.full https://projecteuclid.org/journals/annals-of-applied-statist...