We had 500+ in my graduating class. Three choirs - two were unlimited participation (girl's chorus, full chorus) and the third was "Modern Choir", the audition choir. The senior members of each choir selected the song they would perform. Girl's chorus performed at baccalaureate (yes, all high schools did that back then) and the other two performed during the graduation ceremony. I was in all three choirs; I don't remember what the other two performed, but MC did a piece called "Song of Moses". It was a pretty amazing arrangement but I couldn't find a version on youTube.
It was actually kind of cool the way the ceremony went. Our ceremony was in the Seattle Opera House. The combined band/orchestra played pomp & circumstance (probably about 40 times through!). The seniors marched in alphabetically, and went up on the stage to their seats on risers. As the seniors who were in band got to the front, they moved into their empty seats in the band. It was kind of like the reverse of what the ISU band does on senior night in football.
The sophomores and juniors in the full chorus were also on risers, ready to perform, and those of us who were senior members of the chorus filled out the ends of the rows on the risers. We sang our song after all of the seniors made it onto the stage and into their positions. After we sang, band & chorus seniors went & sat with the rest of the seniors.
TL; DR
Playing a recorded song was not an option for us.