It was not a goodwill gesture, that would totally undermine the bread and butter point to point operation of EI, as you say tickets eligible for through check in are not readily available for purchase on their website. However they can be created by any TA with a GDS and many airlines interline with Aer Lingus in exactly that fashion. You can also achieve the same by booking a multi city itinerary on the EI website.
A TA can use a GDS to create a round the world tirp but short to short connections are not protected by Aer Lingus. You cannot book anywhere from CFN on EI site other than DUB/US even on multi city. Aer Lingus are good at accommodating passengers from EI/EI flights but are not obliged to.
The other airlines have agreements in place with EI and the other airlines will accommodate you on the next leg if EI cause you to miss your connection and they will take the problem up with EI.
EI would of let you use the transit route had it been available however it required a minimum number of passengers and outside T/A there is no way of known numbers and when you are in an industry all about costs they are not going to waste money.
Dublin is the only major airport I've used with a system that makes its transit pax effectively exit the terminal and end up at the check in desks in order to get their next flight.
As you have mentioned this is at least partially due to immigration regulations but still.
Only those with separate tickets.