I understand people would notice a boy's voice was different than a man's, but it's quite a major step to conclude the best way to keep that voice is to castrate that boy. Were there any examples of boys choosing this life, or was this strictly decided by other parties?
What books can a layperson read to learn more about the daily life of castrati?
Are you asking how the castrati as a phenomenon came about, or for stories of how individual boys became castrati? There are probably as many paths to becoming a castrato as there were castrati! But there were boys who chose it, my namesake, Caffarelli, likely chose the life. In his grandmother's will there is a mention of him, she leaves him some money with the note that he would like to study music and desires to become a eunuch. (He was aged 10 at the time of the will.) What agency a 10 year old boy has, I'll leave to you to decide.
There really aren't any good laypeople books about castrati I can recommend uncritically. There is a recent academic book out that's a solid intro, but it's a hard read, I warn you.
I did write a daily life piece though, you might find it interesting!
It's Easter weekend so I will not have time to reply for a while, but I'll be back. :)