Yes, and given the OP agreed with your observation, I can't help but wonder why he didn't mention it in the original post...

I can understand the desire to have his family together, but the policy doesn't seem unreasonable. Satisfying the OP's request would deprive another parent with an infant of a cot. Given his appetite for a cot, perhaps he might have more sympathy for other parents on the flight in the same situation. He's booked well in advance and it seems likely that other infants will join the flight.

The cot positions open up nearer departure. Perhaps that would be a better time to make the request.