I'll always bow out to the pros did the actual design and flying - but this book quote may be one insight.
As the flight deck is over 35 feet above the runway on main wheel touchdown, of key assistance in landing is the radio altimeter. Concorde has two radio altimeters, and on this occasion [early test flight] both failed, so the landing at Fairford....had to be done by eye. It was a 'firm' landing. As Brian Tubshaw put it later: 'We arrived about a half second early.'
The Concorde, Christopher Orlebar, 2017, p. 55
From the point of view of the most critical phase of
human piloting, the radio altimeter was far more important in the scan than the baro altimeter. Baro altitude was generally a problem for the automated part of the envelope, or the FE, while the guys up front needed only spare it a glance (most of the time) only twice a minute or so (or less often?)