Why are the C-C bonds in benzene closer in length to double bonds than single bonds?
one might expect that the bond lengths would be exactly intermediate between a single and a double bond


They actually are. The relevant reference structure, that can provide us lengths of single and double bond for $sp^2$ carbons with not conjugation involved is cyclooctatetraene. The article on the X-ray structure of cycloocta-1,3,5,7-tetrene gives lengths 1.47 and 1.33 angstrom, with their average (1.40) being the exactly value of C-C bond in benzene you provided.