Hi, Dave. Here's an article which gives info about the book and its influences.

https://www.hymnsandcarolsofchristmas.com/Hymns_and_Carols/Biographies/Hadidian/Chap_4-History_%20PC_Songs.htm

The article mentions that many of the songs refer to schools and to singing in school, so I believe that answers many questions about the use of Latin.