I thought, once we got the 3 Black Oaths, the reason was obvious enough why the 'hour of my death" clause is present:
1) I shall obey all commands given by those placed above me in service to the Great Lord; 2) I shall prepare for the day of the Great Lord’s return; and 3) I shall hold close the secrets of the Black Ajah, unto the hour of my death.
1 and 3 contradict each other, if, say, a Darkfriend placed about you orders you to reveal all the Black Ajah's secret. If they swore to never reveal those, period, the two Oaths would contradict, and the Black sister would fall dead.
The "hour of my death" clause gives you the out. Since failing to follow the orders of this person would kill you, the "hour of my death" clause allows Oath 3 to be subordinate to Oath 1. That's why that clause exists.
And yes, the Oath could have been "I shall hold close the secrets of the Black Ajah, unless commanded otherwise by those placed above me in service to the Great Lord", but that leaves the BA beholden completely to anyone placed above them.
The existing Oath, however, has some wiggle room. The BA can negotiate a way out of babbling all secrets right away.
I think it's obviously bad writing, and I doubt very much if the authors gave as much thought to it as you have.
Imagine Alviarin tells Katerine to reveal a single Black Ajah secret to Suian, now. Katerine must immediately do something she has sworn not to do. So now we have a contradiction, and she dies choking. What is it about the extra clause that lets Katerine... wait? The clause doesn't give Katerine permission to delay.
Why does Ishmael want her to live long enough to betray the Black Ajah instead of die immediately anyway?
