This is totally fascinating, but I'm still not sure I get the infrastructural context. Were traditional storm sewers impractical for Chicago at the time specifically because of the city's elevation?
Yep. You need a slope to get water to flow. The city is effectively at lake level. Having a storm sewer doesn't do you much good if the water can't go anywhere.
Another city with similar problems is Berlin, I was there recently and I was puzzled by the crazy pipes all through the centre of the city.
Turns out that the ground water level in Berlin is really high so all construction sites (and there are huge number of these in Berlin) need to pump out the water from excavations which explains the pipes everywhere.
The city _was_ effectively at lake level. Between the raising of Chicago, the Chicago fire (which made sufficient debris to create Grant Park) and additional raising of the street grade, some buildings "ground floors" are three stories above the ground.