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.
Kicks for shoes in general is at least 19th century. It appears to have come from hobo slang (circa 1900s - 1930s), via jazz slang (1920s - 1960s) into African-American slang (1960s -) and from there to more mainstream use, and became used specifically for sneakers/trainers/athletic shoes when these were the most fashionable shoes.
The Concise New Partridge Dictionary of Slang and Unconventional English (2008) says kicks meaning shoes is US from 1897, but has no quotations.
The Oxford English Dictionary dates it to 1904:
1904 ‘No. 1500’ Life in Sing Sing 250/1 Kicks, shoes.
The OED has a pair of 1930s quotations from tramps' slang, followed by John Henrik Clarke's Harlem U.S.A. the story of a city within a city (1964) and a 1973 Black world magazine.
A Jazz Lexicon (1964) by Robert S. Gold says:
kicks, n. pl. i. [from hobo slang: cf. 1930 American Tramp and Underworld Slang, s.v. kicks: "shoes, those things with which a kick is delivered"; current among jazzmen since c. 1925] See 1959 quot. —1958 Somewhere There's Music, p. 101. "She bought me these kicks," he said and held up a foot. — 1959 Swinging Syllables, s.v. kicks: shoes.
The Literary Digest for August 25, 1917 (page 47, Hathitrust) published a letter, dated July 2, from a violin player who had joined the army:
The shoes are great; you can never
know what it is to be comfortable in shoes
until you get into army “kicks." They
_issue us two kinds, hobnails, or field shoes,
and marching shoes, which are just plain,
strong, tan shoes.
A snippet of page 159 of The Rap Attack: African Jive to New York Hip Hop (Pluto Press, 1984) by David Toop gives a rough idea of when and how it was specifically applied to sneakers:
kicks: synonymous with sneakers, which are the last word in footwear. Pumas and Nikes are the current favourites. Example: 'I gotta get me some new kicks to wear to the Funhouse Saturday,' The Funhouse, by the way, is a popular disco with with this crowd.
Best Answer
Etymonline:
And it sounds like a combination of toe and foot.