Conspiracy implies co-operation and planning. The far stronger argument for this is pervasive unconscious bias.

Edit: You added your second sentence after I posted this (that's fine, I do the same sometimes)

And indeed, his slides agree with you. There appears to be no substantial bias towards citing recent work by women. So that doesn't really counter what I said except in the sub-case of older papers.

That sub-case could easily be explained by there being a bias towards citing older work of people considered to be the key people in a field (I would expect so), and a bias against considering women to be the key people in the field. That second bias could be explained by a bias against considering people with female names key people in the field, or it could be considered a bias against considering people with fewer papers (see data/previous arguments for this) key people in the field, or both.

This is a giant unsupported hypothesis. I don't pretend otherwise. It seems to be just as supported as the hypothesis that women are just worse at physics then men though.