It seems rare to have the lead singer record/overdub their own backup vocals in professional settings, but does the quality actually suffer, and does anyone know of any side-by-side comparison?
Honestly it’s rare to have a band with a singer that is capable of recording all the backup vocals. But plenty have.
A lot of the time the backup vocalists are the other band members and they want to record it the way they perform it. Also people have different tones in their voice and it adds color to the song. Same reason guitarists will record rhythm with one rig and leads/solos with another.
Here is a piece from Wikipedia
In the recording studio, some lead singers record their own backing vocals by overdubbing with a multitrack recording system. A multitrack recording system enables the record producer to add many layers of recordings over top of each other. Using a multitrack system, a lead vocalist can record his or her own backing vocals, and then record the lead vocal part over top. Some lead vocalists prefer this approach because the sound of their own harmonies will blend well with their main vocal. One famous example is Freddie Mercury of Queen singing the first part of "Bohemian Rhapsody" himself by overdubbing.1 Patrick Stump of Fall Out Boy, Tom DeLonge of Angels and Airwaves, Wednesday 13 in his own band and Murderdolls, Ian Gillan of Deep Purple, Simon Le Bon of Duran Duran and Brad Delp of Boston also recorded lead and backing vocals for their albums. With the exception of a few songs on each album, Dan Fogelberg, Eddie Rabbitt, David Bowie and Richard Marx sing all of the background vocals for their songs. Robert Smith of the Cure not only sings his own backing vocals in the studio, but also doesn't perform with backing vocalists when playing live.
A lead singer should have a distinctive voice that sticks out. A backup singer should blend in. You'd not want to use autotune on backup tracks.
It's not like there is no use for reusing even a characteristic voice, but then the effect tends to lean more into that of a chorus one rather than lead with backup. A well-known example is Queen's "Bohemian Rhapsody", a studio production on the album "A Night at the Opera" multi-tracking Freddy Mercury as singer.