It should do all that. But then any plants will do that also.
It isn't that the concept doesn't work in freshwater. The reason it is used in saltwater is because nitrate/phosphate removal is more difficult and more important. Corals can be very sensitive to water conditions. As SubRosa mentioned, water changes to simply lower them are expensive. Reactors can be expensive. Saltwater "plants" (macro-algaes) are commonly used but they have their own issues. ATS setups become very appealing at that point since they are cheap and don't include the drawbacks of macro setups.
It isn't that the concept doesn't work in freshwater. The reason it is used in saltwater is because nitrate/phosphate removal is more difficult and more important. Corals can be very sensitive to water conditions. As SubRosa mentioned, water changes to simply lower them are expensive. Reactors can be expensive. Saltwater "plants" (macro-algaes) are commonly used but they have their own issues. ATS setups become very appealing at that point since they are cheap and don't include the drawbacks of macro setups.