There are many historical accounts of freemen in England choosing to become serfs. It wasn’t freedom, but they had real protections. For example they couldn’t be sold individually only the land they where bound to could be sold, which was a major protection keeping families from being broken up.

They may have owed their lord specific quantities of uncompensated labor, but conversely that meant they had socially and legally protected free time.

Also, Serfdom largely disappeared in Western Europe well before America was a thing. “In England, the end of serfdom began with the Peasants' Revolt in 1381. It had largely died out in England by 1500 as a personal status and was fully ended when Elizabeth I freed the last remaining serfs in 1574” “ Serfdom was de facto ended in France by Philip IV, Louis X (1315), and Philip V (1318).[6][7] With the exception of a few isolated cases, serfdom had ceased to exist in France by the 15th century. In Early Modern France, French nobles nevertheless maintained a great number of seigneurial privileges over the free peasants that worked lands under their control. Serfdom was formally abolished in France in 1789.” https://en.wikipedia.org/wiki/History_of_serfdom. Various exceptions did exist but it simply wasn’t that common in Western Europe.