American living in Copenhagen here. We check all of these boxes. The entire channel that runs through town is swimmable thanks to decades of work cleaning it up. On a warm summer day, you could expect maybe 1000+ swimmers in the water in the city centre across all the locations. We also do Vinterbadere (Winter Bathing) throughout the year. The only time you can't swim is after a day or two of sustained rain and there…
Why you can't swim after the rain? Does the water get dirty, or else?
The increase in water discharge also causes sediment to lift from the bed where e coli bacteria live happily in the sediment (think of shaking a bottle with solids that have fallen to the bottom). The potentially harmful bacteria is now suspended in the water for a few days, also growing in number as a result of the runoff nutrients until the increase in the water volume drops and the water can no longer suspend the sediment.
This cycle is the largest reason why, it's not just the runoff (which can also contain animial feces with e coli, etc), it's the runoff with nutrients stirring up the water and lifting e coli which then feasts on the nutrients.
https://www.usgs.gov/publications/escherichia-coli-bacteria-...