That’s a reasonable assumption, but it was already clearly a problem before the Soviet Union collapsed.
IIRC the USSR had planned to line the rivers with concrete and build other devices so there would be less loss.
Those never got built, and there was even less ability to do so after the collapse.
ive heard alternatively that the cotton was important for domestic consumer goods or export in the USSR, in either case they made a short sighted decision that was seen to be more important than the preserving an unexploitable salty sea
they weren't diverted, they were irrigated to shit so there's a ton of existing agriculture that would need paring down, and with climate shit a return to presoviet draw might not even be sufficient.
also they're now 3 capitalist countries that don't cooperate very much so good luck, they'll all accuse each other of cheating & unfairly distributing water. there's no business interests to represent the aral sea either.
Why do that? All or nothing, baby: northern river reversal with atomic bombs!