The United States President has control of American Nuclear weapons. He may have to make a fast decision without having time to consult advisers in an emotionally charged situation. A terrorist disaster killing the three people who should have been president before Byrd was unlikely but possible. Senator Byrd was entitled to stay in the Senate as long as he wanted to and as long as his constituents had confidence in him. There was a strong case for Byrd giving up the position which could have lead to the presidency.
He was older than John McCain, before his death.