The sewers are big because they can contain solid toilet materials which would not fit in a small pipe. It would soon become blocked. In fact, even in large pipes solid materials do not move easily unless there is a lot of water with them.
In general, the people who manage sewers reckon that you need to have at least five times as much water as sewage in the sewers for them to work properly.
It is actually quite easy to know how much water will flow in a sewer. But it is harder to know how much will flow in a storm drain because rainfall is not easy to predict. That is why storm drain sizes are just 'best guesses'.
When the storm drains fill up, the water flows over the street for a while. This is not dangerous, but it must be kept well clear of the sewers because it would be a health risk if sewage got out into the streets.