White was a Democrat and had been appointed by Kennedy, and he thought a Democratic President deserved to appoint his successor.
That may have been the wrong choice, but White had an integrity that so few justices have shown lately.
I'd have thought better of Souter if he'd practiced the same principle and given a Republican a chance to pick his successor.
Also, Potter Stewart was a moderate Republican appointed by Eisenhower who waited until Reagan was elected before stepping down.