The capstan/windlass/pulley/crane (& viticulture & the proceleusmatic metric & much of Western art music's "roots") were invented/developed over 2,500 years ago by the Greeks and Romans. Why wait until circa 1800 for a chanty system?

Answer: We didn't. The modern "practical working" shanty was born with the steam printing press and mass produced sheet music. It is the popular music, vernacular descendant of the Latin lingua franca "celeusma." The latter still means "rower's chant," "sea song" &c in Portuguese, Latin & Greek.

In having popular entertainment to fall back on, Euro-American chanties managed to outlive the steam era altogether.

The more it changes...