“but do Americans”
An American citizen is a sovereign individual and bows to
no one but god. A pope, priest, dictator, king, queen, etc.
is no better than any American citizen and deserve no more
than a handshake if the citizens so wishes.
Slambat, this isn't true of all Americans -- and keep in mind that there are all kinds of bows, with varying shades of meaning.
Even as deracinated 21st century Americans, we know there is the stage-bow by actors, musicians, conductors and performers (at the curtain call) and, in martial arts, ceremonial bows used to begin and end practice and competitions, and to show respect to the instructors, the shihan and the sensei.
Hand-kissing of women by men, in formal settings, includes a bow --- I know that if it were done to me, it would not be adoration (!), although there's a courtly WWII vet at church, an usher, who always opens the church door and bows when he sees me coming: don't tell my husband, but maybe he has a crush? :o)
A large-ish chunk of U.S. Christians belong to churches with recognized customs of bowing, and not just toward God, but also toward altars and tabernacles, Bibles and crosses, other consecrated objects, toward the priests and deacons, and toward each other.
I'm not getting encyclopedic here for no reason. I'm just showing that cultures with a rich repertoire of honor and courtesy, both human and divine, may find it much easier to appreciate bowing and recognize gradations of honor, with a great deal depending on context.