Not to forget, the passport on which you leave one country and the passport on which you enter the next one on the same flight could be different. Consequently, two sets of travel document details for each sector are to be recorded.
How would I currently travel e.g. between the US and Canada if ETA for Canada is registered on a passport other than the one I entered the US with? How will the US authorities know that I left and the Canadian authorities know that I will be coming (and the airline see that I am authorised to do so)?