What water flow conditions might cause a deep, narrow river channel to form
in a stream table?

Steep, high velocity, no silting. The high water speed picks up silt from the bottom instead of letting it settle to the bottom. When the land gets level like often happens at the mouth of rivers where the water spreads out and slows down, silt settles to the bottom and you could get a wide, shallow delta. Around here that silt is probably full of nitrogen fertilizer and the algae blooms. Of course that all depends on the rocks and so forth. If it can not dig, you might get a waterfall.

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