Slavery in Utopia is a “peculiar institution,” though not quite in the way it was in the American South. Slaves in Utopia were either war prisoners, felons (including adulterers!), death row prisoners, or refugees, and Hythloday seems to support this system of slavery because it’s better that someone should perform hard labor than that they should die. Slaves could be released for good behavior and character reform, and their children would not be slaves. In many senses, this slavery is meant as an ethical liberating force, which is extremely ironic (though More would be well before his time to realize such sensibilities.)
“Could it work (or be adapted to work) in a 21st-century society?” I think a look at our prison system and its privatization demonstrates that it certainly is being done in our current society. However, I think it’s extremely socially dysfunctional in a world with currency and other forms of systemic oppression, particularly racism, classism, and sexism (prison being one of the many ways in which patriarchy hurts men, too.) Perhaps it could work in an artificial world without social history but that is not the world we or anyone else lives in. The more that people and resources are commodified, the more oppression that will exist.
I also think Utopian ideas about marriage and divorce very much relate to their system of slavery in that it deals with nonconsensual relationships of ownership, and that breaking the laws related to marriage leads to slavery or banishment from the institution of marriage. We like to joke about the “ball and chain” but the amount of emotional and mental trauma caused by the way we structure romantic relationships is far from funny. I was hoping that Utopia would provide a polyamorous, communal take on romance, but instead, it reified mutually oppressive power structures.

~ Ari Himber