Declan, I really do agree with you in spirit and in fact.

While the geographical history of Ireland is rooted in myth and legend, the use of at least four provinces as geographical descriptions is well attested in the historic records. Even though there may actually have been five provinces historically, as the use of the Irish word coiceda (or fifths) suggests. The ancient provinces found in literary records are Ulster (Ulaid), Connacht, Munster (Mumu), Leinster (Lagin), Meath (Mide).

As you point out, the historic record shows an Ulster which is larger, with a majority Irish nationalist population. However, when the island was partitioned by the British in 1920, the counties of Donegal, Cavan, and Monaghan were gerrymandered to create a unionist majority in the new Protestant Ulster.

Ever since, when the word Ulster has been used synonymously with Northern Ireland, it is used to describe that gerrymandered Protestant Ulster, not historic Ulster. It is disingenous to take the sectarian meaning out of that equation, just because it evokes reactionary feelings about Northern Irish sectarianism among (mostly) British mainlanders.