> Isn't that the basic objection to dark matter, that there's nothing in it that's falsifiable?

I don't think that's case, at least to me it seems that the basic objection is some vague discomfort with the idea, not an issue with the falsifiability. And dark matter is clearly falsifiable, it has already survived many observations.

The CMB power spectrum would look entirely different if there was no dark matter.

Gravitational lensing in certain areas in the sky wouldn't look as strong as it does without dark matter either.