I read that essay, and I think the reason for their existence is simpler: they make face-on mating more comfortable and aesthetically pleasing, which facilitates pair bonding.
One disagreement I have with the OP is in the assertion that permanent breasts would be a necessary disadvantage, ignoring the size issue. Permanent breasts probably evolved gradually, from unnoticeable to male-like to small to the size they are today. A prehistoric hominid female who sprouted D-cups among her flat-chested peers would be at a disadvantage for the reasons the OP gave-- she'd appear infertile at all times-- but the permanent-breasts/no dichotomy is false. The change almost certainly occurred incrementally.
One disagreement I have with the OP is in the assertion that permanent breasts would be a necessary disadvantage, ignoring the size issue. Permanent breasts probably evolved gradually, from unnoticeable to male-like to small to the size they are today. A prehistoric hominid female who sprouted D-cups among her flat-chested peers would be at a disadvantage for the reasons the OP gave-- she'd appear infertile at all times-- but the permanent-breasts/no dichotomy is false. The change almost certainly occurred incrementally.