I don't think people are due to be pushed out of the dome when they turn 70, or whenever, but there are certain positions of authority, such as, oh, I don't know, leadership positions in the US Congress, where maybe there's some responsibility to make sure there are reasonable opportunities for the younger generation. You know, the 60-year-olds.
I don't really what know motivates some like Eliot Engel to try to hold on. Being reasonably *good* at being a House member (which I am not defining as doing stuff I agree with) is actually quite a lot of work, and while senators might get treated like little princes, House members really don't. They don't get that much sycophantic deference. They are one of many and their individual kingdoms are small. Once upon a time the heads of major committees had real power, but that's been eroded over time in various ways.