I am LOVING the idea that the reason my tough ol' great great grandma
had $5,000 to give each grandchild in the 1920s (money that
disappeared in 1929, of course) was because she looked out over the
tributary ditch one day and said, "You know, if I took one of those
bridges they're giving away and put it across the ditch, I could rig
up a pumping system to better irrigate my fields!" But would there
have been ditches WITHOUT such bridges in the first place? How did
you get the water out of the ditch and onto the field without the
bridge/pump system?

Flood irrigation. A system where you divert the stream into a series of
irrigation ditches that water the fields passively without the use of
pumps. In Phoenix AZ, some people have their lawns done this way
instead of using city water. The system was developed by the Anasazi
who no longer inhabit the region. The only down side to that are the
stinking minnows that wind up in the yards.