So far from my research, this seems to be the basic idea; that a person being "waited on hand and foot" has handmaids and footmen (or their equivalents) to perform any manual labor the person would otherwise have to do on their own.
The term may have different but related origins; it could be related to a similar term viewed from the other side, that a person is at someone else's "beck and call", responding immediately to any gesture by the person being served. An extremely attentive servant or corps of same could respond not only to obvious hand gestures, but by more subtle movements of the feet.
Lastly, it's perfectly valid to think of it in the more modern sense of being pampered physically. To "wait on" someone or something is to be immediately available to answer any need. The term may thus have originally been "to wait on someone's hand and foot", thus meaning to have no other duty but to address any need of that hand and/or foot, be it heat, cold, an itch, or in more general terms responding to its every move including as a gesture having meaning. Over time the possessive may have been discarded.