Running water causes a lot more erosion than stationary bodies of water. Consider lakes, which are still cycling water much like a river, but over thousands of years they deposit so much silt that they cease to exist. That’s the opposite of erosion.

Underwater erosion is certainly a thing, but in comparison to downhill water erosion on land, it’s pretty insignificant. It does not seem a given that it could significantly offset the processes that remove salt from salt water.