Is to explain to confused Americans that there is more than one nation by the name of Ireland. And that Dublin is not a war zone ruled by the Queens undead corgis. It persists because it allows for greater specificity when more than one Ireland is under discussion.
Complaining that the Official Official name was not used is strange, because conversations about nations very seldom use the actual official name. Particularly when context craves something else.
For example " There is no United States, its The United States of AMERICA" is certified racist uncle on Thanksgiving territory.
My point with the links was to demonstrate that both “Republic of Ireland” and “The Republic” both have some official standing and usage. As well as a very long history of common usage, including in Ireland. Most of the Irish I know (and there are many) resort to the same terms when discussing the Brexit situation because there is a need to distinguish between the North, the State, and both taken in total. All three can be an commonly are refered simply as “Ireland”, so it can rapidly get weird.