The answer comes down to understanding the difference between sewage treatment and stormwater management.
The Water Environment Federation posted a link to a useful PDF document that summarizes 10 key differences between the two, including why the problems, solutions, and billing mechanisms are different. As they summarized:
Wastewater organizations face unforeseen issues when taking over stormwater programs, many stemming from the fact that, while stormwater seems similar to wastewater, it is actually very different in significant but unappreciated ways.
We have been preparing for several years to understand the challenges of stormwater management and have the plans and resources in place to address the concerns and prepare for the "unforeseen issues" raised in the document linked above.
We have a similar one-page graphic that helps customers understand the difference between our stormwater management program (funded by the stormwater fee beginning this year) and Project Clean Lake, a 25-year plan to reduce pollution in Lake Erie that is funded by your sewer rates: