In Dublin, Amsterdam and Frankfurt I have experienced passport checks on the jetty (or just inside the terminal doors when steps being used). Sometimes it is said these are done on flights with a history of passengers presenting for asylum. Checking at the plane prevents passengers from “losing” their documents on their way to passport control. It’s an additional check and regular passport control has to be passed also.
Border Force / Home Office also do spot checks at the security entrance in BHD, presumably to stop illegal entry to GB after crossing the land border from Ireland. As mentioned above there are regular PSNI checks on arriving passengers into NI from GB (as well as Agriculture checks and Customs).
As to BA not checking IDs in the past on flights to Dublin, they would be running a risk of having to return a passenger back to London. Non UK or Irish Nationals are not able to avail of the free movement provisions of the CTA. The INS in Ireland enforce this at airports and conduct spot checks on public transport on the land border. I’ve had a colleague turned back for not carrying his HK passport. Equally I had a colleague who had a Visa for U.K. but not for Ireland and couldn’t cross the border.
I carry my passport, partly to avoid issues and partly as LHR and LGW occasionally can’t decide if Belfast is domestic or international and send arrivals the wrong way!