I'm doubtful that polygenic scores work, in the sense that we all acknowledge that complex traits like intelligence are interactions between genetics and environment.

You can always decompose a function of two variables into three parts (with some hand-waving for notation):

f(a, b) = f(a) + f(b) + interaction term

where E(interaction term) = 0 in some statistical sense.

If the interaction term is zero, then great, your function is trivially decomposable. For our problem, take a = genetics and b = environment, that means you can precisely talk about someone's 'genetic score for intelligence' and someone's 'environmental score for intelligence', and never have to consider them together.

But I strongly suspect that the interaction between genes and environment is very very high; the latest effort to map genes to intelligence only accounts for 10% of variance not because the environment determines the other 90%, but probably the interaction term, which can be complicated and highly nonlinear.

Another thing: variance of your inputs can only be considered in a statistical sense so the relative importance of genes vs. environment won't be stable. If somehow the world became completely uniform (every single child in the world received the exact same education and upbringing), you'd expect genetic variation to account for everything just by definition.