There are many storm-only drains across the City, some legal/conforming, some not, which empty into assorted rivers/creeks etc.
The real issue is combined sewer overflows CSOs.
Combined sewer overflows result from the storm water off of roads going into the combined sewer with sanitary waste (what you flush); in the 'old City' most sewers are combined rather than separated, so storm water and sanitary water are in the same pipe.
When it rains heavily the emergency design is that these sewers overflow directly into the relevant body of water, untreated.
Sewers in newer parts of the City and new suburbia today are built separated (storm and sanitary flows are in different pipes).
Edit to add:
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The plans now underway to address this:
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