One explanation for the low bridges that's been put forth is that it was cheaper than building high bridges. Makes sense...the original Erie Canal project was financed entirely by NY State ($7 million in the early 1800's) after the federal govt wrote it off as an impractical project that wouldnt benefit the nation even if it were possible to pull off (it was, and it DID).

Interestingly, the refrain in the song "Low Bridge" as originally written is NOT "15 miles on the Erie Canal", but rather, "15 years on the Erie Canal". It went into the folk tradition shortly thereafter, as Hullfish notes, and by 1911, according to one source, it had appeared on a wax cylinder disc as "15 miles....".