Avraham's advanced age is referred to as "zaken ba bayamim" in Ber. 24:1. His age (along with Sarah) is similarly labeled in Ber. 18:11.
Yehoshua is called the same way in Yeh. 13:1 and 23:1, while David Hamelech is called "zaken ba bayamim" in Melachim I, 1:1.
Why are these the only people called "ba bayamim" in reference to their age? What does this phrase add to "zaken" which ties these people together and excludes all others for whom the phrase is not used?